Asymptotics of the mean-field Heisenberg model

Abstract

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 Cramer- 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.

44 pages

References in corpus (3)

• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie--Weiss model
• Rigorous analysis of discontinuous phase transitions via mean-field bounds

Cited by in corpus (5)

• Berry-Esseen Bounds of Normal and Non-normal Approximation for Unbounded Exchangeable Pairs
• Asymptotics of mean-field $O(N)$ models
• Limit Theorems in the Imitative Monomer-Dimer Mean-Field Model via Stein's Method
• Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field
• Error bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models