{"id":8524,"date":"2012-11-19T23:43:17","date_gmt":"2012-11-19T21:43:17","guid":{"rendered":"http:\/\/hgpu.org\/?p=8524"},"modified":"2012-11-19T23:43:17","modified_gmt":"2012-11-19T21:43:17","slug":"criticality-of-the-xy-model-in-complex-topologies","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=8524","title":{"rendered":"Criticality of the XY model in complex topologies"},"content":{"rendered":"<p>The critical behavior of the O(2) model on dilute Levy graphs built on a 2D square lattice is analyzed. Different qualitative cases are probed, varying the exponent rho governing the dependence on the distance of the connectivity probability distribution. The mean-field regime, as well as the long-range and short-range non-mean-field regimes are investigated by means of high-performance parallel Monte-Carlo numerical simulations running on GPUs. The relationship between the long-range rho exponent and the effective dimension of an equivalent short-range system with the same critical behavior is investigated. Evidence is provided for the effective short-range dimension to coincide with the spectral dimension of the Levy graph for the XY model.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The critical behavior of the O(2) model on dilute Levy graphs built on a 2D square lattice is analyzed. Different qualitative cases are probed, varying the exponent rho governing the dependence on the distance of the connectivity probability distribution. The mean-field regime, as well as the long-range and short-range non-mean-field regimes are investigated by means [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[89,3,12],"tags":[196,14,285,20,379,1783,103],"class_list":["post-8524","post","type-post","status-publish","format-standard","hentry","category-nvidia-cuda","category-paper","category-physics","tag-condensed-matter","tag-cuda","tag-numerical-simulation","tag-nvidia","tag-nvidia-geforce-gtx-480","tag-physics","tag-statistical-mechanics"],"views":2280,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8524"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8524\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}