{"id":130496,"date":"2015-10-14T02:00:00","date_gmt":"2015-10-13T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=16af9f58616078d2e7e1e0b7da6b57a1"},"modified":"2015-10-14T02:00:00","modified_gmt":"2015-10-13T23:00:00","slug":"introduction-to-statistical-field-theory-from-a-toy-model-to-a-one-component-plasma","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=130496","title":{"rendered":"Introduction to statistical field theory: from a toy model to a one-component plasma"},"content":{"rendered":"<p>Working with a toy model whose partition function consists of a discrete summation, we introduce the<br \/>\nstatistical field theory methodology by transforming a partition function via a formal Gaussian<br \/>\nintegral relation (the Hubbard\u2013Stratonovich transformation). We then consider Gaussian-type<br \/>\napproximations, wherein correlational contributions enter as harmonic fluctuations around the<br \/>\nsaddle-point solution. This work focuses on how to arrive at a self-consistent, non-perturbative<br \/>\napproximation without recourse to a standard variational construction based on the<br \/>\nGibbs\u2013Bogolyubov\u2013Feynman inequality that is inapplicable to a complex action. To address this<br \/>\nproblem, we propose a construction based on selective satisfaction of a set of exact relations<br \/>\ngenerated by considering a dual representation of a partition function, in its original and<br \/>\ntransformed form.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Working with a toy model whose partition function consists of a discrete summation, we introduce the<br \/>\nstatistical field theory methodology by transforming a partition function via a formal Gaussian<br \/>\nintegral relation (the Hubbard\u2013Stratonovich transfo&#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-130496","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\/130496","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=130496"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/130496\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=130496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=130496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=130496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}