Critical Regime in a Curie-Weiss Model with two Groups and Heterogeneous Coupling

TL;DR

This paper analyzes a two-group Curie-Weiss model at criticality, revealing that the normalized total magnetization converges to a non-Gaussian distribution, extending known results from the single-group case.

Contribution

It extends the understanding of critical behavior in Curie-Weiss models to two groups with heterogeneous coupling, showing non-Gaussian limit distributions.

Findings

Normalized magnetization converges to a non-Gaussian distribution.

Critical regime characterized by $N^{3/4}$ scaling.

Results generalize single-group Curie-Weiss critical behavior.

Abstract

We discuss a Curie-Weiss model with two groups in the critical regime. This is the region where the central limit theorem does not hold any more but the mean magnetization still goes to zero as the number of spins grows. We show that the total magnetization normalized by $N^{3/4}$ converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model.