{"id":6806,"date":"2023-11-08T19:12:50","date_gmt":"2023-11-08T10:12:50","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=6806"},"modified":"2023-11-08T19:12:50","modified_gmt":"2023-11-08T10:12:50","slug":"%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/","title":{"rendered":"\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E7%9B%B8%E8%BB%A2%E7%A7%BB%E3%81%A8%E8%87%A8%E7%95%8C%E7%8F%BE%E8%B1%A1\" >\u76f8\u8ee2\u79fb\u3068\u81e8\u754c\u73fe\u8c61<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E7%90%86%E8%AB%96\" >\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%83%AC%E3%83%97%E3%83%AA%E3%82%AB%E6%B3%95\" >\u30ec\u30d7\u30ea\u30ab\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E9%9B%A2%E6%95%A3%E5%A4%89%E6%95%B0_CSP_%E3%81%AE%E7%9B%B8%E8%BB%A2%E7%A7%BB\" >\u96e2\u6563\u5909\u6570 CSP \u306e\u76f8\u8ee2\u79fb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%82%B8%E3%83%A3%E3%83%9F%E3%83%B3%E3%82%B0%E8%BB%A2%E7%A7%BB\" >\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E8%83%8C%E6%99%AF%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\" >\u80cc\u666f\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E6%89%8B%E6%B3%95%E3%81%A8%E7%B5%90%E6%9E%9C\" >\u624b\u6cd5\u3068\u7d50\u679c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%83%91%E3%83%BC%E3%82%BB%E3%83%97%E3%83%88%E3%83%AD%E3%83%B3%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5b9a\u5f0f\u5316<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E6%A8%A1%E5%9E%8B%E3%81%B8%E3%81%AE%E5%A4%89%E6%8F%9B\" >\u7d71\u8a08\u529b\u5b66\u6a21\u578b\u3078\u306e\u5909\u63db<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E8%AA%BF%E3%81%B9%E3%82%8B%E7%89%A9%E7%90%86%E9%87%8F\" >\u8abf\u3079\u308b\u7269\u7406\u91cf<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E5%9F%BA%E5%BA%95%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC\" >\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%82%AE%E3%83%A3%E3%83%83%E3%83%97%E3%81%AE%E5%88%86%E5%B8%83_gr\" >\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03 $g(r)$<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E5%8A%9B%E3%81%AE%E5%88%86%E5%B8%83_PF\" >\u529b\u306e\u5206\u5e03 $P(F)$<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E8%A8%88%E7%AE%97%E6%96%B9%E6%B3%95\" >\u8a08\u7b97\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E8%A8%88%E7%AE%97%E7%B5%90%E6%9E%9C\" >\u8a08\u7b97\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/%e3%83%91%e3%83%bc%e3%82%bb%e3%83%97%e3%83%88%e3%83%ad%e3%83%b3%e3%81%ae%e3%82%b8%e3%83%a3%e3%83%9f%e3%83%b3%e3%82%b0%e8%bb%a2%e7%a7%bb\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb: The simplest model of jamming<\/li>\n<li>\u8457\u8005: Silvio Franz and Giorgio Parisi<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831: https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8113\/49\/14\/145001<\/li>\n<\/ul>\n<h2 id=\"%E6%A6%82%E8%A6%81\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7d71\u8a08\u529b\u5b66\u3068\u7d44\u5408\u305b\u6700\u9069\u5316\u306e\u95a2\u9023\u306f\u9577\u3089\u304f\u6307\u6458\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u7279\u306b\uff0c\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT) \u3084\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\u306a\u3069\u306e\uff0c\u96e2\u6563\u5909\u6570\u306e <strong>\u5236\u7d04\u5145\u8db3\u554f\u984c<\/strong> (Constraint Satisfaction Problem, \u4ee5\u4e0b CSP) \u306b\u5bfe\u3057\u3066\u306f\uff0c\u7d71\u8a08\u7269\u7406\u5b66\u306e\u89b3\u70b9\u304b\u3089\u306e\u7814\u7a76\u304c\u9032\u3093\u3067\u3044\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c[1] \u3067\u306f\uff0c\u30e9\u30f3\u30c0\u30e0\u306a SAT \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6027\u8cea\u3092\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u6790\u3057\uff0c\u5236\u7d04\u306e\u500b\u6570\u3068\u5909\u6570\u306e\u500b\u6570\u306e\u6bd4\u3092\u5909\u3048\u308b\u3068\u76f8\u8ee2\u79fb\u304c\u8d77\u3053\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\uff0e\u307e\u305f\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u8ee2\u7528\u3057\u3066\uff0cSAT\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u89e3\u304f\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u6848\u3057\u307e\u3057\u305f\uff0e<\/p>\n<p>\u4e00\u65b9\u3067\uff0c\u9023\u7d9a\u5909\u6570 CSP \u306b\u5bfe\u3059\u308b\u7d71\u8a08\u529b\u5b66\u7684\u306a\u7814\u7a76\u306f\u3042\u307e\u308a\u306a\u3055\u308c\u3066\u3044\u307e\u305b\u3093\uff0e\u672c\u8ad6\u6587\u3067\u306f\uff0c\u30ac\u30e9\u30b9\u306e\u30e2\u30c7\u30eb\u3068\u3057\u3066\u7d71\u8a08\u7269\u7406\u5b66\u3067\u7814\u7a76\u3055\u308c\u3066\u3044\u308b\u300c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u300d\u554f\u984c\u304c\uff0c\u9023\u7d9a\u5909\u6570 CSP \u3068\u3057\u3066\u6349\u3048\u3089\u308c\u308b\u3053\u3068\u306b\u7740\u76ee\u3057\u307e\u3059\uff0e\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u306f\u300c<strong>\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb<\/strong>\u300d\u3068\u547c\u3070\u308c\u308b\u76f8\u8ee2\u79fb\u73fe\u8c61\u3092\u793a\u3059\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u672c\u8ad6\u6587\u3067\u306f\uff0c\u9023\u7d9a\u5909\u6570 CSP \u306e\u5358\u7d14\u306a\u4f8b\u3067\u3042\u308b\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u6319\u52d5\u3092\u7d71\u8a08\u529b\u5b66\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u6790\u3057\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3068\u540c\u69d8\u306e\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u304c\u8d77\u3053\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\uff0e<\/p>\n<p>\u672c\u7814\u7a76\u306e\u7d50\u679c\u3088\u308a\uff0c\u591a\u304f\u306e\u9023\u7d9a\u5909\u6570 CSP \u304c\u30b8\u30e3\u30df\u30f3\u30b0\u3068\u3044\u3046\u5171\u901a\u306e\u6027\u8cea\u3092\u6301\u3064\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u307e\u3059\uff0e\u307e\u305f\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3088\u308a\u3082\u6271\u3044\u3084\u3059\u3044\u554f\u984c\u3067\u3042\u308b\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u304c\u30b8\u30e3\u30df\u30f3\u30b0\u73fe\u8c61\u3092\u793a\u3059\u3053\u3068\u304c\u660e\u3089\u304b\u3068\u306a\u3063\u305f\u3053\u3068\u304b\u3089\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u3092\u3088\u308a\u8a73\u7d30\u306b\u8abf\u3079\u308b\u3053\u3068\u3067\uff0c\u30b8\u30e3\u30df\u30f3\u30b0\u306b\u5bfe\u3059\u308b\u7406\u89e3\u304c\u6df1\u307e\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E8%83%8C%E6%99%AF\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3057\u3070\u3089\u304f\uff0c\u80cc\u666f\u3068\u306a\u308b\u7d71\u8a08\u7269\u7406\u5b66\u306e\u77e5\u8b58\u306e\u7c21\u5358\u306a\u8aac\u660e\u3092\u3057\u305f\u306e\u3061\u306b\uff0c\u305d\u308c\u3089\u3092\u307e\u3068\u3081\u3066\u672c\u7814\u7a76\u306e\u8ca2\u732e\u306b\u3064\u3044\u3066\u8ff0\u3079\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E7%9B%B8%E8%BB%A2%E7%A7%BB%E3%81%A8%E8%87%A8%E7%95%8C%E7%8F%BE%E8%B1%A1\"><span class=\"ez-toc-section\" id=\"%E7%9B%B8%E8%BB%A2%E7%A7%BB%E3%81%A8%E8%87%A8%E7%95%8C%E7%8F%BE%E8%B1%A1\"><\/span>\u76f8\u8ee2\u79fb\u3068\u81e8\u754c\u73fe\u8c61<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u76f8\u8ee2\u79fb<\/strong>\u3068\u306f\uff0c\u7269\u7406\u7cfb\u306e\u7269\u7406\u91cf\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u73fe\u8c61\u3067\u3059\uff0e\u4f8b\u3048\u3070\uff0c\u6c34\u306e\u878d\u89e3 (\u56fa\u4f53\u304b\u3089\u6db2\u4f53\u3078\u306e\u5909\u5316) \u3068\u84b8\u767a (\u6db2\u4f53\u304b\u3089\u6c17\u4f53\u3078\u306e\u5909\u5316) \u306f\uff0c\u6c34\u306e\u6e29\u5ea6\u3092\u4e0a\u3052\u3066\u3044\u304f\u306b\u3064\u308c\uff0c\u305d\u308c\u305e\u308c $0$ \u2103\u3068 $100$ \u2103\u3092\u5883\u306b\u6c34\u306e\u5bc6\u5ea6\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u76f8\u8ee2\u79fb\u306e\u4f8b\u3067\u3059\uff0e\u4ed6\u306b\u3082\uff0c\u9244\u304c\u3042\u308b\u6e29\u5ea6\u3067\u5f37\u78c1\u6027 (\u78c1\u77f3\u306b\u304f\u3063\u3064\u304f\u72b6\u614b) \u304b\u3089\u5e38\u78c1\u6027 (\u78c1\u77f3\u306b\u304f\u3063\u3064\u304b\u306a\u3044\u72b6\u614b) \u3078\u5909\u5316\u3059\u308b\u73fe\u8c61\u3082\u76f8\u8ee2\u79fb\u3067\u3059\uff0e<\/p>\n<p><strong>\u81e8\u754c\u73fe\u8c61<\/strong>\u3068\u306f\uff0c\u7269\u7406\u7cfb\u306e\u76f8\u8ee2\u79fb\u70b9\u3067\u306e\u632f\u308b\u821e\u3044\u3067\u3059\uff0e\u8ee2\u79fb\u70b9\u4ed8\u8fd1\u3067\uff0c\u7269\u7406\u91cf\u306f\u3057\u3070\u3057\u3070\u3079\u304d\u4e57\u5247\u306b\u5f93\u3044\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c\u9244\u306e\u5f37\u78c1\u6027\u304b\u3089\u5e38\u78c1\u6027\u3078\u306e\u8ee2\u79fb\u3067\u306f\uff0c\u6e29\u5ea6 $T$ \u306b\u304a\u3044\u3066\u306e\u78c1\u5316 $m(T)$ \u306f\u81e8\u754c\u6e29\u5ea6\u3092 $T_c$ \u3068\u3057\u3066<\/p>\n<p>$$<br \/>\nm(T) \\propto (T_c-T)^\\beta \\<br \/>\n\\beta \\approx 0.325<br \/>\n$$<\/p>\n<p>\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3046\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u3053\u306e\u3079\u304d\u4e57\u5247\u306e\u6307\u6570 $\\beta$ \u306f<strong>\u81e8\u754c\u6307\u6570<\/strong>\u3068\u547c\u3070\u308c\uff0c\u81e8\u754c\u73fe\u8c61\u3092\u7279\u5fb4\u3065\u3051\u308b\u5024\u3068\u3057\u3066\u8208\u5473\u306e\u5bfe\u8c61\u3068\u306a\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u5148\u7a0b\u306e\u81e8\u754c\u6307\u6570 $\\beta \\approx 0.325$ \u306f\uff0c\u9244\u306e\u5f37\u78c1\u6027\u30fb\u5e38\u78c1\u6027\u306e\u8ee2\u79fb\u306b\u7279\u6709\u306e\u5024\u3067\u306f\u306a\u304f\uff0c\u5b9f\u306f\u5f37\u3044\u666e\u904d\u6027\u3092\u6301\u3063\u3066\u3044\u307e\u3059\uff0e\u4ed6\u306e\u591a\u304f\u306e\u7269\u8cea\u306e\u5f37\u78c1\u6027\u30fb\u5e38\u78c1\u6027\u8ee2\u79fb\u3067\u3082\u540c\u3058\u81e8\u754c\u6307\u6570\u3092\u793a\u3059\u3070\u304b\u308a\u304b\uff0c\u4e00\u898b\u5168\u304f\u7570\u306a\u308b\u73fe\u8c61\u3067\u3082\u540c\u3058\u81e8\u754c\u6307\u6570\u3092\u6301\u3064\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u3082\u306e\u304c\u3042\u308a\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c\u6c34\u306e\u6db2\u4f53\u304b\u3089\u6c17\u4f53\u3078\u306e\u8ee2\u79fb\u306b\u304a\u3044\u3066\u5bc6\u5ea6\u306f\u4e0d\u9023\u7d9a\u306b\u5909\u5316\u3057\u307e\u3059\u304c\uff0c\u305d\u306e\u5909\u5316\u91cf\u3092 $\\Delta \\rho(T)$ \u3068\u3059\u308b\u3068\uff0c<\/p>\n<p>$$<br \/>\n\\Delta \\rho(T) \\propto (T_c-T)^\\beta \\<br \/>\n\\beta \\approx 0.325<br \/>\n$$<\/p>\n<p>\u3068\u3044\u3046\uff0c\u5f37\u78c1\u6027\u30fb\u5e38\u78c1\u6027\u8ee2\u79fb\u3068\u540c\u3058\u81e8\u754c\u6307\u6570\u3092\u6301\u3064\u81e8\u754c\u73fe\u8c61\u3092\u793a\u3059\u3053\u3068\u304c\u78ba\u8a8d\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u540c\u3058\u81e8\u754c\u6307\u6570\u3092\u6301\u3064\u7cfb\u306f\u540c\u3058<strong>\u666e\u904d\u6027\u30af\u30e9\u30b9<\/strong>\u306b\u5c5e\u3059\u308b\u3068\u8a00\u308f\u308c\uff0c\u7cfb\u306e\u8a73\u7d30\u306b\u3088\u3089\u306a\u3044\u666e\u904d\u7684\u306a\u6027\u8cea\u3092\u53cd\u6620\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u3055\u307e\u3056\u307e\u306a\u76f8\u8ee2\u79fb\u73fe\u8c61\u3092\u666e\u904d\u6027\u30af\u30e9\u30b9\u3078\u5206\u985e\u3059\u308b\u3053\u3068\u306f\uff0c\u7d71\u8a08\u7269\u7406\u5b66\u306e\u5927\u304d\u306a\u76ee\u6a19\u306e\u4e00\u3064\u3068\u306a\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E7%90%86%E8%AB%96\"><span class=\"ez-toc-section\" id=\"%E3%82%B9%E3%83%94%E3%83%B3%E3%82%B0%E3%83%A9%E3%82%B9%E7%90%86%E8%AB%96\"><\/span>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ising \u6a21\u578b\u306f\uff0c$N$ \u500b\u306e\u30b9\u30d4\u30f3 $s_i$ ($s_i$ \u306f $\\pm 1$ \u306e2\u5024\u3092\u53d6\u308b\u5909\u6570) \u304b\u3089\u306a\u308b\u7cfb\u3067\u3042\u308a\uff0c\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<br \/>\n$$<br \/>\nE({s_i}) = \\sum_{i,j} J_{i,j} s_i s_j<br \/>\n$$<\/p>\n<p>$J_{i,j}$ \u306f\u7d50\u5408\u5b9a\u6570\u3068\u547c\u3070\u308c\uff0c\u30b9\u30d4\u30f3 $s_i$ \u3068 $s_j$ \u306e\u9593\u306e\u76f8\u4e92\u4f5c\u7528\u3092\u8868\u3057\u307e\u3059\uff0e$J_{i,j}&lt;0$ \u306e\u3068\u304d\u306f $s_i,s_j$ \u304c\u540c\u3058\u5411\u304d\u3092\u5411\u304f\u306e\u304c\uff0c$J_{i,j}&gt;0$ \u306e\u3068\u304d\u306f $s_i,s_j$ \u304c\u7570\u306a\u308b\u5411\u304d\u3092\u5411\u304f\u306e\u304c\u305d\u308c\u305e\u308c\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5c0f\u3055\u304f\u306a\u308a\uff0c\u5b89\u5b9a\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>\u7279\u306b\uff0c $J_{i,j}$ \u3092\u8ca0\u306e\u5b9a\u6570\u3068\u3057\u305f\u6700\u3082\u57fa\u672c\u7684\u306a\u6a21\u578b\u306f\uff0c\u78c1\u77f3\u3084\u9244\u306a\u3069\u306e\u5f37\u78c1\u6027\u4f53\u306e\u30e2\u30c7\u30eb\u3068\u3057\u3066\u7528\u3044\u3089\u308c\u307e\u3059\uff0e\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\uff0c\u5404\u30b9\u30d4\u30f3\u306e\u5411\u304d\u304c\u63c3\u3046\u306e\u304c\u5b89\u5b9a\u306a\u72b6\u614b\u3067\u3042\u308a\uff0c\u3053\u308c\u306f\u78c1\u77f3\u306e\u6027\u8cea\u3092\u6349\u3048\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306f\uff0c\u7d50\u5408\u5b9a\u6570 $J_{i,j}$ \u304c\u7d50\u5408\u306b\u3088\u3063\u3066\u30e9\u30f3\u30c0\u30e0\u306a\u5024\u3092\u53d6\u308b\u30e2\u30c7\u30eb\u3067\u3059\uff0e\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\uff0c\u3069\u306e\u3088\u3046\u306b\u30b9\u30d4\u30f3\u306e\u5024\u3092\u6c7a\u3081\u3066\u3082\uff0c $J_{i,j}s_is_j&gt;0$ \u3068\u306a\u308b\u4e0d\u5b89\u5b9a\u306a\u7d50\u5408\u304c\u751f\u3058\u307e\u3059\uff0e\u3053\u306e\u4e0d\u5b89\u5b9a\u3055\u306f\u30d5\u30e9\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3068\u547c\u3070\u308c\uff0c\u3053\u308c\u306b\u3088\u308a\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306f\u8907\u96d1\u306a\u6319\u52d5\u3092\u793a\u3057\u307e\u3059\uff0e\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\uff0c\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u591a\u6570\u306e\u6975\u5c0f\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e\u305d\u308c\u305e\u308c\u306e\u8c37\u306f\u300c<strong>\u72b6\u614b (state)<\/strong>\u300d\u3068\u547c\u3070\u308c\uff0c\u3053\u308c\u3089\u306f\u975e\u5e38\u306b\u5927\u304d\u306a\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u58c1\u3067\u906e\u3089\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<div id=\"attachment_6812\" style=\"width: 568px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6812\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/states-300x165.png\" alt=\"\" width=\"558\" height=\"307\" class=\"wp-image-6812 \" \/><p id=\"caption-attachment-6812\" class=\"wp-caption-text\">\u56f31: \u72b6\u614b\u306e\u6a21\u5f0f\u56f3<\/p><\/div>\n<p>\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u3092\u5206\u6790\u3059\u308b\u624b\u6cd5\u306f\u7d71\u8a08\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u5927\u304d\u304f\u767a\u5c55\u3057\u3066\u3044\u307e\u3059\uff0e\u6b21\u7bc0\u3067\u7d39\u4ecb\u3059\u308b\u30ec\u30d7\u30ea\u30ab\u6cd5\u304c\u4ee3\u8868\u7684\u306a\u624b\u6cd5\u3067\u3059\uff0e<\/p>\n<h3 id=\"%E3%83%AC%E3%83%97%E3%83%AA%E3%82%AB%E6%B3%95\"><span class=\"ez-toc-section\" id=\"%E3%83%AC%E3%83%97%E3%83%AA%E3%82%AB%E6%B3%95\"><\/span>\u30ec\u30d7\u30ea\u30ab\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u672c\u7bc0\u3067\u306f\uff0c\u30ec\u30d7\u30ea\u30ab\u6cd5\u306e\u8a08\u7b97\u306e\u8a73\u7d30\u306b\u306f\u89e6\u308c\u305a\uff0c\u624b\u6cd5\u306e\u30a4\u30e1\u30fc\u30b8\u3092\u5b9a\u6027\u7684\u306b\u8aac\u660e\u3057\u307e\u3059\uff0e\u307e\u305f\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u3067\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3042\u308b\u300c\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u300d\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\uff0e<\/p>\n<p>\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u6a21\u578b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5730\u5f62\u306f\u591a\u304f\u306e\u72b6\u614b\u306b\u5206\u304b\u308c\u307e\u3059\uff0e\u7cfb\u306f\uff0c\u3044\u305a\u308c\u304b\u306e\u72b6\u614b\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u53d6\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e\u305d\u3053\u3067\uff0c\u5404\u72b6\u614b\u306b\u3042\u308b\u7cfb\u306e\u632f\u308b\u821e\u3044\u306e\u5e73\u5747\u5024\u3092\u53d6\u308c\u3070\uff0c\u30e9\u30f3\u30c0\u30e0\u306a\u7cfb\u306e\u5e73\u5747\u7684\u306a\u632f\u308b\u821e\u3044\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<p>\u305d\u3053\u3067\uff0c\u89e3\u6790\u3057\u305f\u3044\u7cfb\u306e\u540c\u4e00\u306e\u30b3\u30d4\u30fc (\u30ec\u30d7\u30ea\u30ab) \u3092\u305f\u304f\u3055\u3093\u4f5c\u3063\u305f\u3068\u3057\u307e\u3057\u3087\u3046\uff0e\u3053\u308c\u3089\u306e\u30ec\u30d7\u30ea\u30ab\u306f\uff0c\u305d\u308c\u305e\u308c\u304c\u3044\u305a\u308c\u304b\u306e\u72b6\u614b\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u53d6\u308a\u307e\u3059\uff0e\u7cfb\u306e\u591a\u6570\u306e\u30ec\u30d7\u30ea\u30ab\u3092\u4e00\u3064\u306e\u5927\u304d\u306a\u7cfb\u3068\u898b\u3066\uff0c\u305d\u306e\u632f\u308b\u821e\u3044\u3092\u8abf\u3079\u308c\u3070\uff0c\u5143\u306e\u7cfb\u306e\u5e73\u5747\u7684\u306a\u632f\u308b\u821e\u3044\u304c\u308f\u304b\u308b\u3067\u3057\u3087\u3046\uff0e\u3053\u308c\u304c\uff0c\u30ec\u30d7\u30ea\u30ab\u6cd5\u306e\u30a2\u30a4\u30c7\u30a2\u3067\u3059\uff0e<\/p>\n<p>\u3082\u3057\uff0c\u72b6\u614b\u304c\u4e00\u3064\u3057\u304b\u306a\u3044\uff0c\u3064\u307e\u308a\u30a8\u30cd\u30eb\u30ae\u30fc\u5730\u5f62\u306b\u8c37\u304c\u4e00\u3064\u3057\u304b\u306a\u3044\u5834\u5408\uff0c\u3059\u3079\u3066\u306e\u30ec\u30d7\u30ea\u30ab\u306f\u540c\u3058\u72b6\u614b\u306b\u5165\u308a\u307e\u3059\uff0e\u3053\u306e\u3068\u304d\uff0c\u3069\u306e\u30ec\u30d7\u30ea\u30ab\u3082\u4e92\u3044\u306b\u533a\u5225\u3067\u304d\u305a\uff0c\u30ec\u30d7\u30ea\u30ab\u306e\u5165\u308c\u66ff\u3048\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3068\u306a\u308a\u307e\u3059\uff0e\u3053\u308c\u3092\u300c<strong>\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027<\/strong>\u300d (Replica Symmetry, RS) \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<p>\u72b6\u614b\u304c\u591a\u6570\u3042\u308b\u5834\u5408\u306f\uff0c\u305d\u308c\u305e\u308c\u306e\u30ec\u30d7\u30ea\u30ab\u304c\u7570\u306a\u308b\u72b6\u614b\u306b\u5165\u308a\uff0c\u30ec\u30d7\u30ea\u30ab\u306e\u5165\u308c\u66ff\u3048\u306b\u3064\u3044\u3066\u306e\u5bfe\u79f0\u6027\u304c\u7834\u308c\u307e\u3059\uff0e\u3053\u308c\u3092\u300c<strong>\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u306e\u7834\u308c<\/strong>\u300d (Replica Symmetry Breaking, RSB) \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E9%9B%A2%E6%95%A3%E5%A4%89%E6%95%B0-csp-%E3%81%AE%E7%9B%B8%E8%BB%A2%E7%A7%BB\"><span class=\"ez-toc-section\" id=\"%E9%9B%A2%E6%95%A3%E5%A4%89%E6%95%B0_CSP_%E3%81%AE%E7%9B%B8%E8%BB%A2%E7%A7%BB\"><\/span>\u96e2\u6563\u5909\u6570 CSP \u306e\u76f8\u8ee2\u79fb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u76f8\u8ee2\u79fb\u3092\u8d77\u3053\u3059\u7cfb\u306f\u7269\u7406\u7cfb\u306b\u9650\u308a\u307e\u305b\u3093\uff0eCSP (\u5236\u7d04\u5145\u8db3\u554f\u984c) \u3082\u76f8\u8ee2\u79fb\u3092\u8d77\u3053\u3059\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>CSP \u3068\u306f\uff0c\u3044\u304f\u3064\u304b\u306e\u5236\u7d04\u3092\u6e80\u305f\u3059\u5909\u6570\u306e\u5024\u306e\u5272\u308a\u5f53\u3066\u304c\u5b58\u5728\u3059\u308b\u304b\u3069\u3046\u304b\u5224\u5b9a\u3059\u308b\u554f\u984c\u3067\u3059\uff0e\u4f8b\u3048\u3070\uff0cK-SAT \u306f\uff0c\u4e0e\u3048\u3089\u308c\u305f\u8ad6\u7406\u5f0f\u3092\u6e80\u305f\u3059\u3088\u3046\u306a\uff0c\u771f\u507d\u5909\u6570\u3078\u306e\u5024\u306e\u5272\u308a\u5f53\u3066\u304c\u5b58\u5728\u3059\u308b\u304b\u5224\u5b9a\u3059\u308b CSP \u3067\u3059\uff0e\u4ed6\u306b\u306f\uff0c\u30b0\u30e9\u30d5\u5f69\u8272\u306f\uff0c\u4e0e\u3048\u3089\u308c\u305f\u30b0\u30e9\u30d5\u306b\u5bfe\u3057\u3066\uff0c\u540c\u3058\u8272\u304c\u96a3\u308a\u5408\u308f\u306a\u3044\u3088\u3046\u306b\u5404\u9802\u70b9\u306b\u8272\u3092\u5272\u308a\u5f53\u3066\u308b CSP \u3067\u3059\uff0e\u307e\u305f\uff0c\u3053\u308c\u3089\u306e\u4f8b\u306f\u3069\u308c\u3082\u5909\u6570\u306e\u5024\u304c\u96e2\u6563\u7684\u306a\u5024\u3092\u53d6\u308b\u305f\u3081\uff0c\u96e2\u6563\u5909\u6570 CSP \u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>\u96e2\u6563\u5909\u6570 CSP \u306f\u3057\u3070\u3057\u3070\u76f8\u8ee2\u79fb\u3092\u8d77\u3053\u3059\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u5909\u6570\u306e\u6570\u3092 $N$, \u5236\u7d04\u306e\u6570\u3092 $M$ \u3068\u3057\uff0c\u6bd4 $\\alpha = M\/N$ \u3092\u5909\u3048\u308b\u3068\uff0c $\\alpha$ \u304c\u5c0f\u3055\u3044\u3068\u304d\u306f\u5236\u7d04\u304c\u5c11\u306a\u304f\uff0c\u5236\u7d04\u306e\u5145\u8db3\u304c\u5bb9\u6613\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\uff0c $\\alpha$ \u304c\u5927\u304d\u3044\u3068\u304d\u306f\u5236\u7d04\u304c\u591a\u304f\uff0c\u3059\u3079\u3066\u306e\u5236\u7d04\u3092\u5145\u8db3\u3059\u308b\u3053\u3068\u304c\u96e3\u3057\u304f\u306a\u308a\u307e\u3059\uff0e $\\alpha$ \u3092\u56fa\u5b9a\u3057\u3066 $N\\to \\infty$ \u306e\u6975\u9650\u3092\u8003\u3048\u308b\u3068\uff0c $\\alpha$ \u304c\u5c0f\u3055\u3044\u9818\u57df\u3067\u306f\u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u53ef\u80fd\u3067\u3042\u308a\uff0c $\\alpha$ \u304c\u5927\u304d\u3044\u9818\u57df\u3067\u306f\u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u4e0d\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\uff0e\u3055\u3089\u306b\uff0c\u5145\u8db3\u53ef\u80fd\u6027\u306e\u5909\u5316\u306f\u6025\u6fc0\u306b\u8d77\u3053\u308a\u307e\u3059\uff0e \u3064\u307e\u308a\uff0c\u3042\u308b\u81e8\u754c\u5024 $\\alpha_c$ \u304c\u5b58\u5728\u3057\u3066\uff0c $\\alpha &lt; \\alpha_c$ \u3067\u306f\u5145\u8db3\u53ef\u80fd\uff0c $\\alpha &gt; \\alpha_c$ \u3067\u306f\u5145\u8db3\u4e0d\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\uff0e\u3053\u306e\u3088\u3046\u306b\uff0c\u5145\u8db3\u53ef\u80fd\u6027\u304c\u6025\u6fc0\u306b\u5207\u308a\u66ff\u308f\u308b\u76f8\u8ee2\u79fb\u3092 <strong>SAT-UNSAT \u8ee2\u79fb<\/strong>\u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<p>\u96e2\u6563\u5909\u6570 CSP \u306f Ising \u6a21\u578b\u306a\u3069\u306e\u96e2\u6563\u7684\u306a\u5909\u6570\u3092\u6301\u3064\u7d71\u8a08\u529b\u5b66\u6a21\u578b\u306b\u7f6e\u304d\u63db\u3048\u3066\u89e3\u6790\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c [1] \u3067\u306f K-SAT \u3092 Ising \u6a21\u578b\u306b\u7f6e\u304d\u63db\u3048\u3066\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u6790\u3057\u3066\u3044\u307e\u3059\uff0e\u8a73\u7d30\u306f<a href=\"\/T-Wave\/?p=6102\">\u8a18\u4e8b<\/a>\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n<h3 id=\"%E3%82%B8%E3%83%A3%E3%83%9F%E3%83%B3%E3%82%B0%E8%BB%A2%E7%A7%BB\"><span class=\"ez-toc-section\" id=\"%E3%82%B8%E3%83%A3%E3%83%9F%E3%83%B3%E3%82%B0%E8%BB%A2%E7%A7%BB\"><\/span>\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb<\/strong>\u306f\uff0c\u8fd1\u5e74\u7d71\u8a08\u7269\u7406\u5b66\u3067\u6ce8\u76ee\u3055\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u76f8\u8ee2\u79fb\u73fe\u8c61\u306e\u4e00\u3064\u3067\u3059\uff0e\u3053\u308c\u306f\uff0c\u7c92\u5b50\u3092\u7a7a\u9593\u306b\u8a70\u3081\u8fbc\u3093\u3060\u3068\u304d\u306b\u8d77\u3053\u308b\u76f8\u8ee2\u79fb\u3067\u3059\uff0e\u7c92\u5b50\u306e\u5bc6\u5ea6\u304c\u5c0f\u3055\u3044\u3068\u304d\u306f\u7c92\u5b50\u304c\u81ea\u7531\u306b\u52d5\u3051\u308b\u306e\u3067\u7cfb\u306f\u6d41\u4f53\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3044\uff0c\u5bc6\u5ea6\u304c\u5927\u304d\u3044\u3068\u304d\u306f\u7c92\u5b50\u304c\u52d5\u3051\u306a\u304f\u306a\u308a\u56fa\u4f53\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3044\u307e\u3059\uff0e\u3053\u306e\u6d41\u4f53\u304b\u3089\u56fa\u4f53\u3078\u306e\u5909\u5316\u306f\u6025\u6fc0\u306b\u8d77\u3053\u308a\u307e\u3059\uff0e<\/p>\n<p>\u4f8b\u3048\u3070\u7802\u6642\u8a08\u3067\u306f\uff0c\u7802\u5c71\u306e\u8868\u9762\u3067\u306f\u7802\u304c\u52d5\u3051\u308b\u306e\u3067\u843d\u3061\u3066\u304d\u305f\u7802\u304c\u6d41\u308c\u308b\u3088\u3046\u306b\u52d5\u304d\u307e\u3059\u304c\uff0c\u7802\u5c71\u306e\u5185\u90e8\u3067\u306f\u5bc6\u5ea6\u304c\u9ad8\u304f\u7802\u306e\u4f4d\u7f6e\u306f\u56fa\u5b9a\u3055\u308c\u3066\u304a\u308a\uff0c\u56fa\u4f53\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3044\u307e\u3059\uff0e<\/p>\n<p>\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u3092\u7814\u7a76\u3059\u308b\u30e2\u30c7\u30eb\u3068\u3057\u3066\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u306e\u304c\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u3067\u3059\uff0e\u3053\u308c\u306f\uff0c\u7403\u72b6\u306e\u7c92\u5b50\u3092\u7bb1\u306b\u5bc6\u5ea6\u3092\u5909\u3048\u306a\u304c\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u8a70\u3081\u8fbc\u3093\u3060\u3068\u304d\u306e\u7cfb\u306e\u632f\u308b\u821e\u3044\u3092\u8abf\u3079\u308b\u554f\u984c\u3067\u3042\u308a\uff0c\u76f8\u8ee2\u79fb\u70b9\u3084\u81e8\u754c\u73fe\u8c61\u304c\u7279\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E8%83%8C%E6%99%AF%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u80cc\u666f\u306e\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7d71\u8a08\u7269\u7406\u5b66\u306e\u69d8\u3005\u306a\u6982\u5ff5\u3092\u7d39\u4ecb\u3057\u305f\u3068\u3053\u308d\u3067\uff0c\u518d\u3073\u672c\u7814\u7a76\u306e\u554f\u984c\u8a2d\u5b9a\u3068\u8ca2\u732e\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305a\uff0c\u76f8\u8ee2\u79fb\u73fe\u8c61\u306f\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5206\u985e\u3067\u304d\u308b\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\u304c\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u306e\u81e8\u754c\u73fe\u8c61\u304c\u3069\u308c\u3060\u3051\u666e\u904d\u7684\u306a\u306e\u304b\u306f\u660e\u3089\u304b\u306b\u306a\u3063\u3066\u3044\u307e\u305b\u3093\uff0e\u305d\u3053\u3067\uff0c\u4ed6\u306b\u3082\u30b8\u30e3\u30df\u30f3\u30b0\u73fe\u8c61\u3092\u793a\u3059\u554f\u984c\u306e\u30af\u30e9\u30b9\u306f\u3042\u308b\u306e\u304b\u3068\u3044\u3046\u3053\u3068\u304c\u8208\u5473\u306e\u5bfe\u8c61\u3068\u306a\u308a\u307e\u3059\uff0e\u307e\u305f\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3068\u540c\u3058\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u304c\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3088\u308a\u3082\u5358\u7d14\u3067\u6271\u3044\u3084\u3059\u3044\u7cfb\u304c\u898b\u3064\u304b\u308c\u3070\uff0c\u305d\u306e\u5358\u7d14\u306a\u7cfb\u3092\u8a73\u3057\u304f\u8abf\u3079\u308b\u3053\u3068\u3067\u30b8\u30e3\u30df\u30f3\u30b0\u73fe\u8c61\u306b\u3064\u3044\u3066\u306e\u7406\u89e3\u304c\u6df1\u307e\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p>\u6b21\u306b\uff0c\u96e2\u6563\u5909\u6570 CSP \u304c\u76f8\u8ee2\u79fb\u73fe\u8c61\u3092\u793a\u3059\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\uff0e\u4e00\u65b9\u3067\uff0c\u9023\u7d9a\u5909\u6570 CSP \u306b\u3064\u3044\u3066\u306f\u3042\u307e\u308a\u7814\u7a76\u304c\u306a\u3055\u308c\u3066\u3044\u306a\u3044\u306e\u304c\u73fe\u72b6\u3067\u3059\uff0e\u9023\u7d9a\u5909\u6570 CSP \u306f\u96e2\u6563\u5909\u6570 CSP \u3068\u540c\u69d8\u306b\u76f8\u8ee2\u79fb\u73fe\u8c61\u3092\u793a\u3059\u306e\u304b\uff0c\u793a\u3059\u306a\u3089\u3070\uff0c\u3069\u306e\u3088\u3046\u306a\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u306e\u304b\uff0c\u3068\u3044\u3046\u70b9\u306e\u89e3\u660e\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p>\u672c\u7814\u7a76\u306f\uff0c\u4ee5\u4e0a2\u3064\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\uff0e\u5177\u4f53\u7684\u306b\u306f\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u3068\u3044\u3046\u30b7\u30f3\u30d7\u30eb\u306a\u9023\u7d9a\u5909\u6570\u306e CSP \u306e SAT-UNSAT \u8ee2\u79fb\u3092\u89e3\u6790\u3057\uff0c\u3053\u308c\u304c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u306e\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u3068\u540c\u3058\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E6%89%8B%E6%B3%95%E3%81%A8%E7%B5%90%E6%9E%9C\"><span class=\"ez-toc-section\" id=\"%E6%89%8B%E6%B3%95%E3%81%A8%E7%B5%90%E6%9E%9C\"><\/span>\u624b\u6cd5\u3068\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 id=\"%E3%83%91%E3%83%BC%E3%82%BB%E3%83%97%E3%83%88%E3%83%AD%E3%83%B3%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%83%BC%E3%82%BB%E3%83%97%E3%83%88%E3%83%AD%E3%83%B3%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u554f\u984c\u3067\u3059\uff0e<\/p>\n<ul>\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec{X} \\in \\mathbb{R}^N$ \u3068\uff0c\u4e0e\u3048\u3089\u308c\u305f $M$ \u500b\u306e\u30d1\u30bf\u30fc\u30f3 $\\vec{\\xi^\\mu} \\in \\mathbb{R}^N , (\\mu=1,\\dots,M)$ \u3068\u306e\u5185\u7a4d\u3092\u5b9a\u6570 $\\kappa$ \u4ee5\u4e0a\u306b\u3067\u304d\u308b\u304b\uff1f<\/li>\n<\/ul>\n<p>\u3053\u306e\u554f\u984c\u3092\uff0c $N$ \u5909\u6570 $M$ \u5236\u7d04\u306eCSP\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u5f0f\u5316\u3067\u304d\u307e\u3059\uff0e<\/p>\n<ul>\n<li>\u6b21\u306e\u5236\u7d04\u3092\u6e80\u305f\u3059 $\\vec{X} \\in \\mathbb{R}^N$ \u3092\u6c42\u3081\u3088<\/li>\n<li>\u5236\u7d04:<br \/>\n$$\\vec{X} \\cdot \\vec{X}=N \\ r_\\mu\\equiv\\frac{1}{\\sqrt{N}} \\vec{X} \\cdot \\vec{\\xi^\\mu} &#8211; \\kappa \\geq 0,,(\\mu=1,2,\\dots,M)$$<\/li>\n<\/ul>\n<p>$r_\\mu$ \u3092\u30ae\u30e3\u30c3\u30d7\u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<p>\u3053\u306e\u554f\u984c\u306f\uff0c $\\kappa$ \u306e\u7b26\u53f7\u306b\u3088\u3063\u3066\u6027\u8cea\u304c\u5927\u304d\u304f\u7570\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>($\\kappa \\geq 0$ \u306e\u3068\u304d)<\/p>\n<p>\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306f2\u5024\u5206\u985e\u554f\u984c\u3068\u898b\u306a\u305b\u307e\u3059\uff0e2\u5024\u5206\u985e\u554f\u984c\u3068\u306f\uff0c $M$ \u500b\u306e\u30c7\u30fc\u30bf\u304b\u3089\u306a\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 ${(\\vec{x^\\mu}, y^\\mu) \\mid \\mu=1,2,\\dots,M} , (\\vec{x^\\mu} \\in \\mathbb{R}^N, y^\\mu \\in {+1, -1})$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\uff0c $y^\\mu=+1$ \u306a\u3089 $\\vec{w} \\cdot \\vec{x^\\mu} \\gt 0$, $y^\\mu=-1$ \u306a\u3089 $\\vec{w} \\cdot \\vec{x^\\mu} \\lt 0$ \u3068\u306a\u308b\u3088\u3046\u306a\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec{w} \\in \\mathbb{R}^N$ \u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3059\uff0e $\\vec{\\xi^\\mu}=y^\\mu \\vec{x^\\mu}$ \u3068\u3057\u3066\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u554f\u984c\u3092\u89e3\u3044\u305f\u3068\u304d\u306e\u89e3 $\\vec{X}$ \u306f2\u5024\u5206\u985e\u554f\u984c\u306e\u89e3 $\\vec{w}$ \u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0c $\\kappa \\geq 0$ \u306e\u3068\u304d\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u554f\u984c\u306f\u51f8\u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff0e\u3064\u307e\u308a\uff0c2\u3064\u306e\u89e3\u3092\u53d6\u3063\u305f\u3068\u304d\u306b\uff0c\u305d\u308c\u3089\u306e\u4e2d\u9593\u3082\u307e\u305f\u89e3\u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff0e\u51f8\u6700\u9069\u5316\u554f\u984c\u306f\u7c21\u5358\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>($\\kappa &lt; 0$ \u306e\u3068\u304d)<\/p>\n<p>\u3053\u306e\u554f\u984c\u306f\u975e\u51f8\u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff0e\u3064\u307e\u308a\uff0c2\u3064\u306e\u89e3\u306e\u4e2d\u9593\u304c\u89e3\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\uff0e\u4e00\u822c\u306b\uff0c\u975e\u51f8\u306a\u554f\u984c\u306e\u6700\u9069\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\uff0e<\/p>\n<h3 id=\"%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E6%A8%A1%E5%9E%8B%E3%81%B8%E3%81%AE%E5%A4%89%E6%8F%9B\"><span class=\"ez-toc-section\" id=\"%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E6%A8%A1%E5%9E%8B%E3%81%B8%E3%81%AE%E5%A4%89%E6%8F%9B\"><\/span>\u7d71\u8a08\u529b\u5b66\u6a21\u578b\u3078\u306e\u5909\u63db<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b21\u306b\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u554f\u984c\u3092\u7d71\u8a08\u529b\u5b66\u6a21\u578b\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u554f\u984c\u306b\u5e30\u7740\u3055\u305b\u307e\u3059\uff0e\u5236\u7d04\u304c\u3059\u3079\u3066\u5145\u8db3\u3055\u308c\u3066\u3044\u308c\u3070\u30a8\u30cd\u30eb\u30ae\u30fc\u304c $0$\uff0c\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u5236\u7d04\u304c\u5b58\u5728\u3059\u308c\u3070\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u6b63\u3068\u306a\u308b\u3088\u3046\u306a\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u8a2d\u8a08\u3059\u308c\u3070\u3088\u3044\u3067\u3059\uff0e<\/p>\n<p>\u5236\u7d041\u3064\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092<br \/>\n$$v(r) = \\frac{1}{2}r^2 \\theta(-r)$$<br \/>\n\u3068\u3057\u307e\u3059\uff0e\u3053\u3053\u3067\uff0c $\\theta(x)$ \u306f\u30b9\u30c6\u30c3\u30d7\u95a2\u6570 ($x\\geq 0$ \u3067 $1$, $x&lt;0$ \u3067 $0$) \u3067\u3059\uff0e $v(r)$ \u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<div id=\"attachment_6813\" style=\"width: 593px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6813\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/energy-300x227.png\" alt=\"\" width=\"583\" height=\"441\" class=\" wp-image-6813\" \/><p id=\"caption-attachment-6813\" class=\"wp-caption-text\">\u56f32: \u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u30b0\u30e9\u30d5<\/p><\/div>\n<p>\u5168\u4f53\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\uff0c\u5404\u5236\u7d04\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u7dcf\u548c\u3068\u3057\u307e\u3059 $$H[\\vec{X}]=\\displaystyle \\sum_{\\mu=1}^M v(r_\\mu)$$<\/p>\n<p>$H[\\vec{X}]=0$ \u3067\u3042\u308b\u3053\u3068\u3068\uff0c $\\vec{X}$ \u304c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u554f\u984c\u306e\u89e3\u3067\u3042\u308b\u3053\u3068\u306f\u540c\u5024\u3067\u3059\uff0e\u3053\u308c\u306b\u3088\u308a\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5145\u8db3\u53ef\u80fd\u6027\u3092\u8abf\u3079\u308b\u3053\u3068\u306f\uff0c $H[\\vec{X}]$ \u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8abf\u3079\u308b\u3053\u3068\u306b\u5e30\u7740\u3057\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E8%AA%BF%E3%81%B9%E3%82%8B%E7%89%A9%E7%90%86%E9%87%8F\"><span class=\"ez-toc-section\" id=\"%E8%AA%BF%E3%81%B9%E3%82%8B%E7%89%A9%E7%90%86%E9%87%8F\"><\/span>\u8abf\u3079\u308b\u7269\u7406\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4 id=\"%E5%9F%BA%E5%BA%95%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC\"><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E5%BA%95%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC\"><\/span>\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\uff0c\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8abf\u3079\u308b\u3053\u3068\u306f\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5145\u8db3\u53ef\u80fd\u6027\u3092\u8abf\u3079\u308b\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff0e\u307e\u305f\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf\u6570\u3068\u30d1\u30bf\u30fc\u30f3\u6570\u306e\u6bd4 $\\alpha := M\/N$ \u3084 $\\kappa$ \u306e\u5024\u3092\u56fa\u5b9a\u3057\uff0c\u30e9\u30f3\u30c0\u30e0\u306a\u30d1\u30bf\u30fc\u30f3\u306b\u5bfe\u3059\u308b\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5e73\u5747\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3067\uff0cSAT-UNSAT \u8ee2\u79fb\u3092\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5e73\u5747\u5024\u304c $0$ \u3067\u3042\u308c\u3070\uff0c\u305d\u306e $(\\alpha,\\kappa)$ \u306e\u7d44\u306fSAT\u76f8\u306b\u3042\u308a\uff0c\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5e73\u5747\u5024\u304c $0$ \u3088\u308a\u5927\u304d\u3051\u308c\u3070\uff0c\u305d\u306e $(\\alpha,\\kappa)$ \u306e\u7d44\u306fUNSAT\u76f8\u306b\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<h4 id=\"%E3%82%AE%E3%83%A3%E3%83%83%E3%83%97%E3%81%AE%E5%88%86%E5%B8%83-gr\"><span class=\"ez-toc-section\" id=\"%E3%82%AE%E3%83%A3%E3%83%83%E3%83%97%E3%81%AE%E5%88%86%E5%B8%83_gr\"><\/span>\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03 $g(r)$<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u4ed6\u306b\u3082\uff0cSAT-UNSAT\u8ee2\u79fb\u70b9\u4ed8\u8fd1\u3067\u306e\u7cfb\u306e\u632f\u308b\u821e\u3044\uff0c\u3059\u306a\u308f\u3061\u81e8\u754c\u73fe\u8c61\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\uff0e\u305d\u308c\u3089\u3092\u7279\u5fb4\u3065\u3051\u308b\u7269\u7406\u91cf\u3092\u3044\u304f\u3064\u304b\u8abf\u3079\u307e\u3059\uff0e<\/p>\n<p>\u4e00\u3064\u306f\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03\u3067\u3059\uff0e $r_\\mu\\geq 0$ \u306e\u3068\u304d\uff0c $r_\\mu$ \u306e\u5024\u306f\u5236\u7d04 $\\mu$ \u304c\u3069\u308c\u3060\u3051\u4f59\u88d5\u3092\u6301\u3063\u3066\u5145\u8db3\u3055\u308c\u3066\u3044\u308b\u304b\u3092\u8868\u3057\u307e\u3059\uff0e\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03 $g(r)$ \u3068\u306f\uff0c $M$ \u500b\u306e\u5236\u7d04\u306e\u3046\u3061\uff0c\u30ae\u30e3\u30c3\u30d7\u304c $r$ \u3068\u306a\u308b\u3082\u306e\u306e\u5272\u5408\u3092\u8868\u3057\u307e\u3059\uff0e<\/p>\n<p>\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u3067\u306f\uff0c $r$ \u304c\u5c0f\u3055\u3044\u9818\u57df\u3067\u306f $g(r)$ \u304c\u3079\u304d\u4e57\u5247 $g(r) \\propto r^{-\\gamma}$ \u306b\u5f93\u3046\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u304a\u308a\uff0c\u81e8\u754c\u6307\u6570 $\\gamma \\approx 0.413$ \u304c\u5831\u544a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5834\u5408\u3082 $g(r)$ \u306f\u3079\u304d\u4e57\u5247\u306b\u5f93\u3046\u306e\u304b\u8abf\u3079\uff0c\u305d\u3046\u306a\u3089\u3070\u81e8\u754c\u6307\u6570\u306e\u5024\u3092\u7279\u5b9a\u3059\u308b\u3053\u3068\u304c\u76ee\u6a19\u3067\u3059\uff0e<\/p>\n<h4 id=\"%E5%8A%9B%E3%81%AE%E5%88%86%E5%B8%83-pf\"><span class=\"ez-toc-section\" id=\"%E5%8A%9B%E3%81%AE%E5%88%86%E5%B8%83_PF\"><\/span>\u529b\u306e\u5206\u5e03 $P(F)$<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03\u304c\uff0c\u5145\u8db3\u3055\u308c\u3066\u3044\u308b\u5236\u7d04\u306b\u95a2\u3059\u308b\u91cf\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\uff0c\u529b\u306e\u5206\u5e03\u306f\uff0c\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u5236\u7d04\u306b\u95a2\u3059\u308b\u91cf\u3067\u3059\uff0e<\/p>\n<p>\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\uff0c\u3059\u306a\u308f\u3061 $r_\\mu \\lt 0$ \u3067\u3042\u308b\u5404\u5236\u7d04\u306f\uff0c\u305d\u306e\u5236\u7d04\u3092\u6e80\u305f\u3059\u65b9\u5411\u306b\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec{X}$ \u3092\u52d5\u304b\u305d\u3046\u3068\u3059\u308b\u529b\u3092\u53ca\u307c\u3057\u307e\u3059\uff0e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $H$ \u304c $r_\\mu$ \u306e2\u6b21\u5f0f\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304b\u3089\uff0c\u5236\u7d04 $\\mu$ \u304c $\\vec{X}$ \u306b\u53ca\u307c\u3059\u529b $F_\\mu$ \u306f $\\vert r_\\mu \\vert$ \u306b\u6bd4\u4f8b\u3057\u307e\u3059\uff0e\u3088\u3063\u3066\uff0c\u529b\u306e\u5f37\u3055\u306f\uff0c\u5236\u7d04\u304c\u3069\u308c\u304f\u3089\u3044\u306e\u5f37\u3055\u3067\u9055\u53cd\u3055\u308c\u3066\u3044\u308b\u304b\u3092\u8868\u3057\u307e\u3059\uff0e\u529b\u306e\u5206\u5e03 $P(F)$ \u306f\uff0c $M$ \u500b\u306e\u5236\u7d04\u306e\u3046\u3061\uff0c\u529b\u306e\u5927\u304d\u3055\u304c $F$ \u3068\u306a\u308b\u3082\u306e\u306e\u5272\u5408\u3092\u8868\u3057\u307e\u3059\uff0e<\/p>\n<p>\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u306b\u304a\u3051\u308b\u529b\u306e\u5206\u5e03\u306f\uff0c\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03\u3068\u540c\u69d8\u306b\uff0c $F$ \u304c\u5c0f\u3055\u3044\u9818\u57df\u3067\u3079\u304d\u4e57\u5247 $P(F) \\propto F^\\theta$ \u306b\u5f93\u3044\uff0c\u81e8\u754c\u6307\u6570 $\\theta \\approx 0.423$ \u304c\u5831\u544a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u305d\u3053\u3067\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u529b\u306e\u5206\u5e03\u306f\u3069\u306e\u3088\u3046\u306b\u632f\u308b\u821e\u3046\u306e\u304b\u3092\u672c\u8ad6\u6587\u3067\u306f\u89e3\u6790\u3057\u307e\u3059\uff0e<\/p>\n<h3 id=\"%E8%A8%88%E7%AE%97%E6%96%B9%E6%B3%95\"><span class=\"ez-toc-section\" id=\"%E8%A8%88%E7%AE%97%E6%96%B9%E6%B3%95\"><\/span>\u8a08\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>$\\alpha = M\/N$ \u3068 $\\kappa$ \u306e\u5024\u3092\u56fa\u5b9a\u3057\u3066\uff0c \u30d1\u30bf\u30fc\u30f3 ${\\vec{\\xi}^\\mu}_{\\mu=1,2,\\dots,M}$ \u3092 Gauss \u5206\u5e03\u306b\u5f93\u3063\u3066\u30e9\u30f3\u30c0\u30e0\u306b\u751f\u6210\u3057\u305f\u3068\u304d\u306e\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5404\u7269\u7406\u91cf\u306e\u5e73\u5747\u5024\u3092\u8abf\u3079\u307e\u3059\uff0e<\/p>\n<p>\u8a08\u7b97\u306b\u306f\u30ec\u30d7\u30ea\u30ab\u6cd5\u3092\u7528\u3044\u307e\u3059\uff0e $\\kappa \\geq 0$ \u306b\u3064\u3044\u3066\u306f\u5148\u884c\u7814\u7a76 [2] \u304c\u3042\u308a\u307e\u3059\u304c\uff0c\u672c\u8ad6\u6587\u3067\u306f $\\kappa &lt; 0$ \u306e\u9818\u57df\u3082\u89e3\u6790\u3057\u307e\u3059\uff0e<\/p>\n<p>\u8a08\u7b97\u306e\u6d41\u308c\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\uff0e<\/p>\n<ol>\n<li>RS \u4eee\u5b9a (\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u304c\u7834\u308c\u3066\u3044\u306a\u3044\uff0c\u3059\u306a\u308f\u3061\u89e3\u7a7a\u9593\u3067\u72b6\u614b\u306f\u4e00\u3064\u3057\u304b\u306a\u3044\u3068\u4eee\u5b9a) \u3067\u8a08\u7b97\u3059\u308b<\/li>\n<li>RS \u89e3\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308b\u9818\u57df\u3092\u6c42\u3081\u308b<\/li>\n<li>RS \u89e3\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308b\u9818\u57df\u3067\uff0c RSB \u4eee\u5b9a (\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u304c\u7834\u308c\u3066\u3044\u308b\uff0c\u3059\u306a\u308f\u3061\u89e3\u7a7a\u9593\u3067\u72b6\u614b\u306f\u8907\u6570\u306b\u5206\u88c2\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u4eee\u5b9a) \u3067\u8a08\u7b97\u3059\u308b<\/li>\n<\/ol>\n<p>\u8a08\u7b97\u306e\u8a73\u7d30\u306f\u8ad6\u6587\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n<h3 id=\"%E8%A8%88%E7%AE%97%E7%B5%90%E6%9E%9C\"><span class=\"ez-toc-section\" id=\"%E8%A8%88%E7%AE%97%E7%B5%90%E6%9E%9C\"><\/span>\u8a08\u7b97\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u76f8\u56f3\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\uff0e<\/p>\n<div id=\"attachment_6815\" style=\"width: 582px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6815\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/phase_diagram-300x218.png\" alt=\"\" width=\"572\" height=\"416\" class=\" wp-image-6815\" \/><p id=\"caption-attachment-6815\" class=\"wp-caption-text\">\u56f33: \u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u76f8\u56f3 (https:\/\/iopscience.iop.org\/article\/10.1088\/1751-8113\/49\/14\/145001)<\/p><\/div>\n<p><img decoding=\"async\" src=\"phase_diagram.png\" alt=\"\" \/><\/p>\n<p>\u9752\u7dda\u306f SAT-UNSAT \u8ee2\u79fb\u70b9\u3092\u8868\u3057\u3066\u304a\u308a\uff0c\u9752\u7dda\u306e\u4e0b\u5074\u3067\u306f SAT, \u4e0a\u5074\u3067\u306f UNSAT \u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>\u8d64\u7dda\u306f\uff0cRS \u89e3\u304c\u4e0d\u5b89\u5b9a\u306b\u306a\u308b dAT (de Almeida-Thouless) \u7dda\u3092\u8868\u3057\u3066\u3044\u307e\u3059\uff0e\u8d64\u7dda\u306e\u4e0b\u5074\u3067\u306f RS \u89e3\u306f\u5b89\u5b9a\u3067\u3042\u308a\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u89e3\u306e\u5b58\u5728\u9818\u57df\u306f\u9023\u7d50\u3067\u3059\uff0e\u8d64\u7dda\u306e\u4e0a\u5074\u3067\u306f RS \u89e3\u306f\u4e0d\u5b89\u5b9a\u3067\u3042\u308a\uff0c\u89e3\u306e\u5b58\u5728\u9818\u57df\u306f\u7d30\u304b\u304f\u5206\u88c2\u3057\u307e\u3059\uff0e\u306a\u304a\uff0c\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u306e\u7834\u308c\u304c\u8d77\u3053\u308b\u306e\u306f $\\kappa \\lt 0$ \u306e\u9818\u57df\u306e\u307f\u3067\u3042\u308a\uff0c $\\kappa \\geq 0$ \u3067\u306f\u3059\u3079\u3066\u306e $\\alpha$ \u3067RS\u89e3\u304c\u5b89\u5b9a\u3067\u3059\uff0e\u3053\u308c\u306f\uff0c $\\kappa \\geq 0$ \u3067\u306f\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u89e3\u304c\u51f8\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3082\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<p>\u6b21\u306b\uff0c SAT-UNSAT \u8ee2\u79fb\u70b9\u306b\u304a\u3051\u308b\u81e8\u754c\u73fe\u8c61\u3092\u8abf\u3079\u307e\u3057\u305f\uff0e $\\kappa \\geq 0$ \u306e\u9818\u57df\u3067\u306f\uff0c\u81e8\u754c\u73fe\u8c61\u306f\u8d77\u3053\u308a\u307e\u305b\u3093\u3067\u3057\u305f\uff0e\u3059\u306a\u308f\u3061\uff0c\u30ae\u30e3\u30c3\u30d7\u306e\u5206\u5e03 $g(r)$ \u3084\u529b\u306e\u5206\u5e03 $P(F)$ \u306f\u3079\u304d\u4e57\u5247\u306b\u5f93\u3044\u307e\u305b\u3093\u3067\u3057\u305f\uff0e\u4e00\u65b9\u3067\uff0c $\\kappa \\lt 0$ \u306e\u9818\u57df\u3067\u306f\u81e8\u754c\u73fe\u8c61\u304c\u8d77\u3053\u308a\uff0c $r$ \u304c\u5c0f\u3055\u3044\u9818\u57df\u3067 $g(r) \\propto r^{-\\gamma}, , \\gamma \\approx 0.413, , P(F) \\propto F^{\\theta}, , \\theta \\approx 0.423$ \u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e\u3053\u308c\u3089\u306e\u5024\u306f\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u306e\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u306b\u304a\u3051\u308b\u81e8\u754c\u6307\u6570\u3068\u4e00\u81f4\u3057\u307e\u3059\uff0e\u3053\u306e\u767a\u898b\u3088\u308a\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306f $\\kappa \\lt 0$ \u3067\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3068\u540c\u3058\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<\/p>\n<h2 id=\"%E7%B5%90%E8%AB%96\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u7814\u7a76\u3067\u306f\uff0c\u9023\u7d9a\u5909\u6570 CSP \u306e\u6700\u3082\u5358\u7d14\u306a\u4f8b\u306e\u4e00\u3064\u3067\u3042\u308b\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u3092\u89e3\u6790\u3057\u307e\u3057\u305f\uff0e\u305d\u306e\u7d50\u679c\uff0c $\\kappa \\lt 0$ \u306e\u975e\u51f8\u9818\u57df\u3067\u306f\uff0c\u81e8\u754c\u73fe\u8c61\u304c\u898b\u3089\u308c\uff0c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3068\u540c\u3058\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<\/p>\n<p>\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u3088\u308a\u3082\u30b7\u30f3\u30d7\u30eb\u3067\u89e3\u6790\u3057\u3084\u3059\u3044\u6a21\u578b\u3067\u3042\u308b\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u304c\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u3068\u540c\u3058\u3088\u3046\u306a\u76f8\u8ee2\u79fb\u3092\u793a\u3059\u3053\u3068\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u305f\u3053\u3068\u306b\u3088\u308a\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u6027\u8cea\u3092\u66f4\u306b\u8abf\u3079\u308b\u3053\u3068\u3067\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u306b\u5bfe\u3059\u308b\u3055\u3089\u306a\u308b\u77e5\u898b\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0c\u3053\u306e\u7d50\u679c\u3088\u308a\uff0c\u4ed6\u306e\u591a\u304f\u306e\u975e\u51f8\u306a\u9023\u7d9a\u5909\u6570 CSP \u3082\u540c\u3058\u666e\u904d\u6027\u30af\u30e9\u30b9\u306b\u5c5e\u3059\u308b\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u307e\u3059\uff0e\u4ed6\u306e\u9023\u7d9a\u5909\u6570 CSP \u306b\u5bfe\u3057\u3066\u3082\uff0c\u672c\u7814\u7a76\u306e\u3088\u3046\u306a\u89e3\u6790\u3092\u884c\u3046\u3053\u3068\u3067\uff0c\u3053\u306e\u4e88\u60f3\u3092\u691c\u8a3c\u3059\u308b\u3053\u3068\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30ec\u30d7\u30ea\u30ab\u6cd5\u306e\u8a08\u7b97\u3092\u8ffd\u3046\u306e\u304c\u5927\u5909\u3067\u3057\u305f (\u307e\u3060\u4e00\u90e8\u8ffd\u3044\u5207\u308c\u3066\u3044\u307e\u305b\u3093)\uff0e<\/p>\n<p>\u3053\u306e\u7814\u7a76\u3067\u306f\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u89e3\u3092\u6c42\u3081\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u306f\u89e6\u308c\u3089\u308c\u3066\u3044\u307e\u305b\u3093\uff0e\u7279\u306b\uff0c\u89e3\u306e\u51f8\u6027\u304c\u5931\u308f\u308c\uff0c\u30ec\u30d7\u30ea\u30ab\u5bfe\u79f0\u6027\u304c\u7834\u308c\u308b\u9818\u57df\u3067\u306f\uff0c\u65e2\u5b58\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u89e3\u304f\u3053\u3068\u304c\u96e3\u3057\u304f\u306a\u308b\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u307e\u3059\uff0eK-SAT \u306e\u5834\u5408\u306f\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u306e\u624b\u6cd5\u3092\u8ee2\u7528\u3057\u3066\uff0cRSB \u9818\u57df\u3067\u3082\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u69cb\u6210\u3067\u304d\u307e\u3057\u305f\u304c\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306b\u5bfe\u3057\u3066\u3082\u540c\u69d8\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u3067\u304d\u308b\u306e\u304b\u306f\u6c17\u306b\u306a\u308b\u3068\u3053\u308d\u3067\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0c\u591a\u5c64\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u5834\u5408\u3067\u89e3\u6790\u3059\u308b\u3053\u3068\u3082\u9762\u767d\u305d\u3046\u3060\u3068\u601d\u3044\u307e\u3059\uff0e\u591a\u5c64\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u89e3\u7a7a\u9593\u306e\u69cb\u9020\u306b\u5bfe\u3059\u308b\u77e5\u898b\u304c\u5f97\u3089\u308c\u308c\u3070\uff0c\u73fe\u4ee3\u306e\u6df1\u5c64\u5b66\u7fd2\u306e\u6210\u529f\u3092\u8aac\u660e\u3059\u308b\u624b\u304c\u304b\u308a\u306b\u306a\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff0e<\/p>\n<h2 id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>[1] Mezard, M., &amp; Zecchina, R. (2002). <em>The random K-satisfiability problem: from an analytic solution to an efficient algorithm<\/em>. https:\/\/doi.org\/10.1103\/PhysRevE.66.056126<\/p>\n<p>[2] Gardner, E., &amp; Derrida, B. (1988). Optimal storage properties of neural network models. <em>Journal of Physics A: Mathematical and General<\/em>, <em>21<\/em>(1), 271\u2013284. https:\/\/doi.org\/10.1088\/0305-4470\/21\/1\/031<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7d71\u8a08\u529b\u5b66\u3068\u7d44\u5408\u305b\u6700\u9069\u5316\u306e\u95a2\u9023\u306f\u9577\u3089\u304f\u6307\u6458\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u7279\u306b\uff0c\u5145\u8db3\u53ef\u80fd\u6027\u554f\u984c (SAT) \u3084\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\u306a\u3069\u306e\uff0c\u96e2\u6563\u5909\u6570\u306e \u5236\u7d04\u5145\u8db3\u554f\u984c (Constraint Satisfaction Problem, \u4ee5\u4e0b CSP) \u306b\u5bfe\u3057\u3066\u306f\uff0c\u7d71\u8a08\u7269\u7406\u5b66\u306e\u89b3\u70b9\u304b\u3089\u306e\u7814\u7a76\u304c\u9032\u3093\u3067\u3044\u307e\u3059\uff0e\u4e00\u65b9\u3067\uff0c\u9023\u7d9a\u5909\u6570 CSP \u306b\u5bfe\u3059\u308b\u7d71\u8a08\u529b\u5b66\u7684\u306a\u7814\u7a76\u306f\u3042\u307e\u308a\u306a\u3055\u308c\u3066\u3044\u307e\u305b\u3093\uff0e\u672c\u8ad6\u6587\u3067\u306f\uff0c\u30ac\u30e9\u30b9\u306e\u30e2\u30c7\u30eb\u3068\u3057\u3066\u7d71\u8a08\u7269\u7406\u5b66\u3067\u7814\u7a76\u3055\u308c\u3066\u3044\u308b\u300c\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u300d\u554f\u984c\u304c\uff0c\u9023\u7d9a\u5909\u6570 CSP \u3068\u3057\u3066\u6349\u3048\u3089\u308c\u308b\u3053\u3068\u306b\u7740\u76ee\u3057\u307e\u3059\uff0e\u7403\u306e\u30d1\u30c3\u30ad\u30f3\u30b0\u306f\u300c\u30b8\u30e3\u30df\u30f3\u30b0\u8ee2\u79fb\u300d\u3068\u547c\u3070\u308c\u308b\u76f8\u8ee2\u79fb\u73fe\u8c61\u3092\u793a\u3059\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u672c\u8ad6\u6587\u3067\u306f\uff0c\u9023\u7d9a\u5909\u6570 CSP 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