{"id":182,"date":"2015-07-26T20:39:44","date_gmt":"2015-07-26T11:39:44","guid":{"rendered":"http:\/\/alprovs.dip.jp\/wordpress\/?p=182"},"modified":"2021-08-19T09:32:27","modified_gmt":"2021-08-19T00:32:27","slug":"%e3%83%9d%e3%83%83%e3%83%84%e3%83%a2%e3%83%87%e3%83%ab%e3%81%ae%e6%ad%b4%e5%8f%b2%ef%bc%88%e6%88%90%e7%ab%8b%e3%81%a1%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.alprovs.com\/wordpress\/?p=182","title":{"rendered":"\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u306e\u6b74\u53f2\uff08\u6210\u7acb\u3061\uff09"},"content":{"rendered":"

\u4eca\u56de\u306f\uff0c\u524d\u306b\u300c\u7814\u7a76\u9032\u6357\u72b6\u6cc1 2015.07.21<\/a>\u300d\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\uff0c\u7814\u7a76\u3057\u3066\u3044\u308b\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u306e\u6b74\u53f2\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u308b\u3002<\/p>\n

\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u3078\u3068\u3064\u306a\u304c\u308b\u6700\u521d\u306e\u7814\u7a76\u306f\uff0c 1943\u5e74 Ashkin \u3068 Teller [1] \u306b\u3088\u3063\u30662\u6b21\u5143\u6b63\u65b9\u683c\u5b50\u306e\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u30924\u72b6\u614b\u3078\u3068\u62e1\u5f35\u3057\u305f\u30e2\u30c7\u30eb<\/del>4\u72b6\u614b\u306e\u30e2\u30c7\u30eb<\/span>\u306b\u3064\u3044\u3066\u7814\u7a76\u304c\u884c\u308f\u308c\u305f\u3002\u6b21\u306b\uff0c1952\u5e74\u306b\u540d\u524d\u306e\u7531\u6765\u3068\u306a\u3063\u305f Potts \u304c\u4ee5\u4e0b\u306b\u7d9a\u304f\u7814\u7a76[4]\u3092\u884c\u3063\u305f\u3002Potts \u306f\uff0cKramers \u3068 Wannier \u306e\u65b9\u6cd5[2][3]\u3092\u4f7f\u7528\u3057\uff0c\u30b9\u30d4\u30f3\u306e\u65b9\u5411\u3092\u89d2\u5ea6\u3068\u307f\u306a\u3057\u3066q\u72b6\u614b\u306b\u62e1\u5f35\u3057\u305f<\/p>\n


\n$$ \\mathcal{H} = – \\sum _{ \\langle ij \\rangle } J( \\Theta _{ij} ) $$<\/center>
\n\uff08\u3053\u3053\u3067<\/p>\n


\n$$ \\Theta _{ij} = \\Theta _{n_i} – \\Theta _{n_j} , \\Theta _n = 2 \\pi n \/ q, n = 0,1, \\ldots , q-1 $$<\/center>
\n\u3067\u3042\u308a\uff0c\u548c\u306f\u96a3\u63a5\u3057\u305f\u683c\u5b50\u70b9\u306b\u3064\u3044\u3066\u884c\u3046\u3068\u3044\u3046\u610f\u5473\uff09\u3068\u3044\u3046\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066<\/p>\n


\n$$ J( \\Theta ) = \\varepsilon _1 \\cos \\Theta $$<\/center>
\n\u306e\u6642\uff0cq = 2,3,4 \u306e\u6b63\u65b9\u683c\u5b50\u3064\u3044\u3066\u306e\u81e8\u754c\u70b9\u3092\u6c7a\u5b9a\u3057\u305f\u3002\u3053\u306e\u3068\u304dq > 4\u3067\u306e\u81e8\u754c\u70b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u304b\u3063\u305f\u304c\uff0c<\/p>\n


\n$$ J( \\Theta ) = \\varepsilon _2 \\delta _{Kr} ( n_i , n_j ) $$<\/center>
\n\u306e\u7279\u5225\u306a\u5834\u5408\u306b\u304a\u3044\u3066\u306f\u3059\u3079\u3066\u306eq\u306b\u3064\u3044\u3066\u306e\u81e8\u754c\u70b9\u304c\u63a8\u91cf\u3055\u308c\u305f\u3002\u305d\u3057\u3066\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u3068\u3044\u3046\u540d\u524d\u306f\uff08\u8ad6\u6587\u3092\u8aad\u3093\u3067\u3044\u306a\u3044\u306e\u3067\u5206\u304b\u3089\u306a\u3044\u304c\uff091974\u5e74\u306b Domb \u306b\u3088\u3063\u3066\u63d0\u6848[5]\u3055\u308c\u305f\u3088\u3046\u3060\u30021\u3064\u76ee\u306eJ(\u0398)\u306e\u5f62\u306f planar Potts model \u3068\u547c\u3070\u308c\uff0c2\u3064\u76ee\u306f standard Potts model \u3068\u547c\u3070\u308c\u308b\u3002\u901a\u5e38\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u3068\u547c\u3070\u308c\u308b\u306e\u306f\u5f8c\u8005\u306e\u307b\u3046\u3067\u3042\u308b\u3002\uff08\u4ed6\u306b\u3082\u8272\u3005\u3068\u547c\u3073\u65b9\u306f\u3042\u308b\u307f\u305f\u3044\u3060\uff09<\/p>\n

\u6570\u5f0f\u306f[6]\u3088\u308a\u5f15\u7528<\/p>\n

Refarences
\n[1] J. Ashkin and E. Teller, Phys. Rev. 64, 178 (1943).
\n[2] Kramers, H. A. and Wannier, G. H., Phys. Rev. 60, 252 (1941)
\n[3] Kramers, H. A. and Wannier, G. H., Phys. Rev. 60, 263 (1941)
\n[4] Potts, R. B., Proc. Camb. Phil. Soc. 48, 106 (1952)
\n[5] Domb, C., J. Phys. A 7, 1335 (1974)
\n[6] F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982)<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4eca\u56de\u306f\uff0c\u524d\u306b\u300c\u7814\u7a76\u9032\u6357\u72b6\u6cc1 2015.07.21\u300d\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\uff0c\u7814\u7a76\u3057\u3066\u3044\u308b\u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u306e\u6b74\u53f2\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u308b\u3002 \u30dd\u30c3\u30c4\u30e2\u30c7\u30eb\u3078\u3068\u3064\u306a\u304c\u308b\u6700\u521d\u306e\u7814\u7a76\u306f\uff0c 1943\u5e74 Ashkin \u3068 Teller [1] \u306b\u3088\u3063\u30662\u6b21 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-182","post","type-post","status-publish","format-standard","hentry","category-2"],"_links":{"self":[{"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=182"}],"version-history":[{"count":28,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/182\/revisions"}],"predecessor-version":[{"id":824,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/182\/revisions\/824"}],"wp:attachment":[{"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.alprovs.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}