Asymptotics of the Mean-Field Heisenberg Model

Kay Kirkpatrick, Elizabeth Meckes

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)54-92
Number of pages39
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jul 2013


  • Gibbs measures
  • Heisenberg model
  • Phase transition
  • Statistical mechanics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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