We present an improved finite-size scaling method for reliably extracting the critical temperature T_BKT of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using the known Weber-Minhagen multiplicative logarithmic correction to the spin stiffness rho_s at T_BKT and the Kosterlitz-Nelson relation between the transition temperature and the stiffness, rho_s(T_BKT)=2T_BKT\/pi, we define a size dependent transition temperature T_ BKT(L_1,L_2) based on a pair of system sizes L1, L2, e.g., L_2=2L1. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved, rapidly convergent, and can be reliably extrapolated to the thermodynamic limit, L_1,L_2 -> infinity. Using GPU (graphical processing unit) computing, we obtain high-precision data for L up to 512 and extract a transition temperature T_BKT=0.89274(1), where the statistical error, +\/- 1, in the last digit is about 6 times smaller than that of the best previous estimate.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present an improved finite-size scaling method for reliably extracting the critical temperature T_BKT of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using the known Weber-Minhagen multiplicative logarithmic correction to the spin stiffness rho_s at T_BKT and the Kosterlitz-Nelson relation between the transition temperature and the stiffness, rho_s(T_BKT)=2T_BKT\/pi, we define a size dependent transition temperature T_ BKT(L_1,L_2) based […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","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":[196,14,20,1783,103,1382],"class_list":["post-8932","post","type-post","status-publish","format-standard","hentry","category-nvidia-cuda","category-paper","category-physics","tag-condensed-matter","tag-cuda","tag-nvidia","tag-physics","tag-statistical-mechanics","tag-tesla-c2090"],"views":3008,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8932","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=8932"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8932\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}