Two Groups in a Curie-Weiss Model

TL;DR

This paper investigates the behavior of two disjoint groups of spins in a Curie-Weiss model, demonstrating law of large numbers for their sums and conditions under which the central limit theorem applies.

Contribution

It establishes the law of large numbers for two groups of spins and identifies temperature conditions for the central limit theorem in this setting.

Findings

Law of large numbers holds for both groups' sums

Central limit theorem applies only at low inverse temperatures

Results depend on the homogeneity of the coupling matrix

Abstract

We show for two disjoint groups of spins in a Curie-Weiss model and a homogeneous coupling matrix that the law of large numbers holds for the normed sums of both groups' spin variables. We also show that the central limit theorem holds only for low inverse temperatures.