{"id":301,"date":"2021-09-17T11:38:40","date_gmt":"2021-09-17T03:38:40","guid":{"rendered":"http:\/\/49.235.202.190\/?p=301"},"modified":"2021-09-17T12:02:15","modified_gmt":"2021-09-17T04:02:15","slug":"%e7%a7%91%e7%a0%94%e8%af%be%e5%a0%82%ef%bc%88%e4%ba%8c%ef%bc%89-%e5%b9%b3%e5%9d%87%e5%9c%ba%e8%bf%91%e4%bc%bc%e5%92%8cising%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/shuaiwang.cc\/?p=301","title":{"rendered":"\u79d1\u7814\u8bfe\u5802\uff08\u4e8c\uff09\u2014\u2014\u5e73\u5747\u573a\u8fd1\u4f3c\u548cIsing\u6a21\u578b"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u7b2c\u4e00\u8282\u8bfe\u4e3b\u8981\u662f\u53d9\u8ff0\u4e86\u201c\u76f8\u201d\u7684\u6982\u5ff5\u4ee5\u53ca\u4e24\u79cd\u4e0d\u540c\u7684\u76f8\u8fb9\u754c\u6a21\u578b\uff08diffusive interface vs sharp interface\uff09\u3002\u7b2c\u4e8c\u8282\u8bfe\u7684\u4e3b\u9898\u662f\u76f8\u53d8\uff08phase transition\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f8\u53d8\u662f\u4e00\u4e2a\u975e\u5e73\u8861\u8fc7\u7a0b\uff0c\u63cf\u8ff0\u8d77\u6765\u6bd4\u5e73\u8861\u8fc7\u7a0b\u8981\u590d\u6742\u3002\u6211\u4eec\u4ece\u6700\u7b80\u5355\u7684Ising\u6a21\u578b\u5165\u624b\uff0c\u5bf9\u76f8\u53d8\u8fdb\u884c\u523b\u753b\u3002\u867d\u7136\u6570\u5b66\u6a21\u578b\u8f83\u4e3a\u7b80\u5355\uff0c\u4f46\u662f\u597d\u5904\u662f\u53ef\u4ee5\u5b9a\u6027\u5730\u5206\u6790\u7cfb\u7edf\u7684\u7279\u5f81\u6e29\u5ea6\u3001\u76f8\u53d8\u65f6\u5bf9\u5e94\u7684\u5b8f\u89c2\u7269\u7406\u91cf\u7684\u53d8\u5316\u3002\u662f\u7814\u7a76\u590d\u6742\u76f8\u53d8\u8fc7\u7a0b\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ising \u6a21\u578b\u6700\u4e3b\u8981\u7684\u5047\u8bbe\u6709\u4e24\u4e2a\uff1a <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u72b6\u6001\u53ea\u6709\u4e24\u79cd +1 -1 \uff08\u66f4\u4e3a\u590d\u6742\u7684\u60c5\u51b5\uff0c\u72b6\u6001\u53ef\u4ee5\u63cf\u8ff0\u4e3a\u77e2\u91cf\u7b49\u8fde\u7eed\u53d8\u5316\u7684\u91cf\u3001\u751a\u81f3\u53ef\u4ee5\u63cf\u8ff0\u4e3a\u6ce2\u51fd\u6570\uff09<\/li><li>\u5047\u8bbe\u7c92\u5b50\u53ea\u4e0e\u6700\u8fd1\u7684\u7c92\u5b50\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\uff08\u5373\u53ea\u5b58\u5728\u8fd1\u573a\u76f8\u4e92\u4f5c\u7528\uff0c\u65e0\u957f\u7a0b\u4f5c\u7528\uff09<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u4e8e\u8fd9\u4e24\u70b9\u51fa\u53d1\uff0c\u53ef\u4ee5\u7ed9\u51fa\u81ea\u65cb\u7c92\u5b50\u7684\u54c8\u5bc6\u987f\u91cf\u3002\u4ece\u54c8\u5bc6\u987f\u91cf\u51fa\u53d1\u3001\u7ed3\u5408Gibbs\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\uff08\u6982\u7387\u4f9d\u80fd\u91cf\u6307\u6570\u5206\u914d\uff09\uff0c\u53ef\u63a8\u5012\u51fa\u7c92\u5b50\u81ea\u65cb\u91cf\u7684\u6982\u7387\u6d4b\u5ea6\uff08tanh\u5206\u5e03\uff0cslide-12\uff09\u3002\u5f97\u5230\u81ea\u65cb\u7684\u6982\u7387\u5206\u5e03\uff0c\u5c31\u53ef\u4ee5\u63a8\u51fa\u4e00\u7cfb\u5217\u7684\u5b8f\u89c2\u7269\u7406\u91cf\u3002\u5982net magnetization\u3001\u80fd\u91cf\u3001\u78c1\u6ede\u56de\u7ebf\u7b49\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\u95ee\u9898\u7684\u6838\u5fc3\u5c31\u5728\u4e8e\u5982\u4f55\u89e3\u51fa\u81ea\u65cb\u7684\u6982\u7387\u5206\u5e03\uff1f\u5e73\u5747\u573a\u8fd1\u4f3c\u5047\u8bbe\uff1a<strong>\u6bcf\u4e2a\u7c92\u5b50\u6240\u53d7\u5230\u7684\u5916\u754c\u4f5c\u7528\uff08\u8bfe\u5802\u4e0a\u7684\u4f8b\u5b50\u662f\u5916\u754c\u78c1\u573a\u4f5c\u7528\uff09\u662f\u5468\u56f4\u6240\u6709\u7c92\u5b50\u7684\u5e73\u5747\u3002<\/strong>\u56e0\u6b64\u5728\u516c\u5f0f\uff085\uff09\u4e2d\uff0c\u53ef\u4ee5\u5c06\\(q_i\\)\u7528\\(&lt;q&gt;\\)\u4ee3\u66ff\u3002\u7ecf\u8fc7\u8fd9\u79cd\u65b9\u6cd5\u5904\u7406\uff0c\u65b9\u7a0b\u5927\u4e3a\u7b80\u5316\uff08\u4e0d\u9700\u8981\u8003\u8651\u5468\u56f4\u7c92\u5b50\u7684\u53cd\u8f6c\u7b49\u77ac\u6001\u8fc7\u7a0b\uff09\u7531\u5e73\u5747\u573a\u8fd1\u4f3c\u53ef\u4ee5\u5f97\u51fa\u4e00\u7cfb\u5217\u5f88\u597d\u7684\u7ed3\u679c\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u76f8\u53d8\u6e29\u5ea6Tc<\/li><li>\u76f8\u53d8\u78c1\u573aHc<\/li><li>\u78c1\u6ede\u56de\u7ebf<\/li><li>\u533a\u5206\u4e00\u7ea7\u76f8\u53d8\u4e8c\u7ea7\u76f8\u53d8<\/li><li>\\(&lt;q&gt; ~ (T_c-T)^{0.5}\\)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e73\u5747\u573a\u8fd1\u4f3c\u662f\u4e0d\u7cbe\u786e\u7684\u3002Onsager\u7ed9\u51fa\u4e86\u4e8c\u7ef4Ising\u6a21\u578b\u7684\u89e3\u6790\u63a5\uff0c\u5e8f\u53c2\u91cf\u7684critical exponent\u503c\u4e0d\u662f0.5\uff0c\u800c\u662f0.125 \u3002[1]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ed9\u540c\u5b66\u4eec\u7559\u4e0b\u7684\u4f5c\u4e1a\u662f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\u3001\u56de\u53bb\u52a8\u624b\u7b97\u4e00\u4e0b\\(\\tanh (Ax+b) = x\\)\u7684\u89e3\u3002\u6211\u7528\u7684\u662f\u76f4\u63a5\u8fed\u4ee3\u3002\u5982\u679c\u7528\u725b\u987f\u8fed\u4ee3\u662f\u4e0d\u662f\u6536\u655b\u6027\u66f4\u597d\uff1f\u53ef\u5426\u7528\u7a0b\u5e8f\u8bc1\u660e\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2\u3001\u7b97\u4e00\u4e0b\\(T^* = 0\\) \u548c\\(T^* &gt; 0)\u65f6\u5019\u7684\u78c1\u6ede\u56de\u7ebf\uff0c\u770b\u4e00\u4e0b\u4e0e\u4f4e\u6e29\u65f6\u5019\u6709\u4f55\u533a\u522b\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8d44\u6599\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a  data-e-Disable-Page-Transition=\"true\" class=\"download-link\" title=\"\" href=\"https:\/\/shuaiwang.cc?download=302&amp;tmstv=1782163750\" rel=\"nofollow\" id=\"download-link-302\" data-redirect=\"false\" >\n\t[\u7b2c\u4e8c\u8282\u8bfe\u8bfe\u4ef6]<\/a>\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a  data-e-Disable-Page-Transition=\"true\" class=\"download-link\" title=\"\" href=\"https:\/\/shuaiwang.cc?download=311&amp;tmstv=1782163750\" rel=\"nofollow\" id=\"download-link-311\" data-redirect=\"false\" >\n\t[\u8ba1\u7b97\u4e0d\u540c\u6e29\u5ea6\u4e0b\u7684<q>]<\/a>\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a  data-e-Disable-Page-Transition=\"true\" class=\"download-link\" title=\"\" href=\"https:\/\/shuaiwang.cc?download=314&amp;tmstv=1782163750\" rel=\"nofollow\" id=\"download-link-314\" data-redirect=\"false\" >\n\t[\u8ba1\u7b97\u78c1\u6ede\u56de\u7ebf\u7684python\u7a0b\u5e8f]<\/a>\n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">python\u73af\u5883\u7ba1\u7406\u5305\uff1aanaconda: https:\/\/www.anaconda.com\/<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">python\u7684IDE\uff1aspyder \u53ef\u4ee5\u5728anaconda\u4e2d\u4e0b\u8f7d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6709\u7528\u7684\u5305\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u81ea\u884c\u641c\u7d22\u624b\u518c\u3001\u53ef\u7528anaconda\u5b89\u88c5\u6216\u8005\u7528pip\u5b89\u88c5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u672c\u6570\u5b66\u5de5\u5177\u548c\u6570\u7ec4\uff1anumpy <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u79d1\u5b66\u8ba1\u7b97\u3001\u6c42\u89e3\u65b9\u7a0b\uff1a scipy \uff08\u90e8\u5206\u66ff\u4ee3mathematica\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u636e\u8868\uff1a pandas \uff08\u53ef\u66ff\u4ee3excel\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ed8\u56fe\uff1amatplotlib \uff08\u53ef\u66ff\u4ee3origin\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53c2\u8003\u6587\u732e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Onsager, Lars. &#8220;Crystal statistics. I. A two-dimensional model with an order-disorder transition.&#8221;&nbsp;<em>Physical Review<\/em>&nbsp;65.3-4 (1944): 117.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c\u4e00\u8282\u8bfe\u4e3b\u8981\u662f\u53d9\u8ff0\u4e86\u201c\u76f8\u201d\u7684\u6982\u5ff5\u4ee5\u53ca\u4e24\u79cd\u4e0d\u540c\u7684\u76f8\u8fb9\u754c\u6a21\u578b\uff08diffusive interface vs sha &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/shuaiwang.cc\/?p=301\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u79d1\u7814\u8bfe\u5802\uff08\u4e8c\uff09\u2014\u2014\u5e73\u5747\u573a\u8fd1\u4f3c\u548cIsing\u6a21\u578b\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,12],"tags":[],"class_list":["post-301","post","type-post","status-publish","format-standard","hentry","category-uncategorized","category-12","entry"],"_links":{"self":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=301"}],"version-history":[{"count":3,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/301\/revisions"}],"predecessor-version":[{"id":318,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=\/wp\/v2\/posts\/301\/revisions\/318"}],"wp:attachment":[{"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/shuaiwang.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}