Asymptotics of the Mean-Field Heisenberg Model

被引：0
作者：
Kay Kirkpatrick
Elizabeth Meckes
机构：
[1] University of Illinois at Urbana-Champaign,Department of Mathematics
[2] Case Western Reserve University,Department of Mathematics
来源：
Journal of Statistical Physics | 2013年 / 152卷
关键词：
Statistical mechanics; Gibbs measures; Phase transition; Heisenberg model;
D O I：
暂无
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学科分类号：
摘要：
We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramér- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein’s method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
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页码：54 / 92
页数：38
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