Two Groups in a Curie-Weiss Model with Heterogeneous Coupling

Abstract

We discuss a Curie-Weiss model with two groups with different coupling constants within and between groups. For the total magnetisations in each group, we show bivariate laws of large numbers and a central limit theorem which is valid in the high temperature regime. In the critical regime, the total magnetisation normalised by $N^{3/4}$ converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model. Finally, we prove a kind of a `law of large numbers' in the low temperature regime, more precisely we prove that the empirical magnetisation converges in distribution to a mixture of two Dirac measures.

The third version contains some new results as well as the critical regime results from arXiv:1807.05020

References in corpus (3)

• Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach
• Scaling Limits for Multispecies Statistical Mechanics Mean-Field Models
• Rescaled Magnetization for Critical Bipartite Mean-Fields Models