{"id":337205,"date":"2016-12-13T03:00:00","date_gmt":"2016-12-13T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=fcdb13b4d949ed72ba7dbac8dfb2e545"},"modified":"2016-12-13T03:00:00","modified_gmt":"2016-12-13T00:00:00","slug":"combinatorial-approach-to-exactly-solve-the-1d-ising-model","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=337205","title":{"rendered":"Combinatorial approach to exactly solve the 1D Ising model"},"content":{"rendered":"<p>The Ising model is a well known statistical model which can be solved exactly by various methods.<br \/>\nThe most familiar one is the transfer matrix method. Sometimes it can be difficult to approach the<br \/>\nopen boundary case rather than periodic boundary ones in higher dimensions. But physically it is<br \/>\nmore intuitive to study the open boundary case, as it gives a closer view of the real system. We<br \/>\nhave introduced a new method called the pairing method to determine the exact partition function for<br \/>\nthe simplest case, a 1D Ising lattice. This method simplifies the problem&#8217;s complexities and reduces<br \/>\nit to a pure combinatorial problem. The study also reveals that it is possible to apply this pairing<br \/>\nmethod in the case of a 2D square lattice. The obtained results agree perfectly with the values in<br \/>\nthe literature and this new approach provides an algorithmic insight to deal with such problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Ising model is a well known statistical model which can be solved exactly by various methods.<br \/>\nThe most familiar one is the transfer matrix method. Sometimes it can be difficult to approach the<br \/>\nopen boundary case rather than periodic boundary ones&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-337205","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/337205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=337205"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/337205\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=337205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=337205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=337205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}