Limit Theorems for Multi-Group Curie-Weiss Models via the Method of Moments

TL;DR

This paper extends the Curie-Weiss spin model to multiple groups, analyzing its behavior across different temperature regimes using the method of moments, with potential applications in social sciences.

Contribution

It introduces a multi-group Curie-Weiss model and applies the method of moments to characterize its asymptotic behavior across regimes.

Findings

Identification of three temperature regimes in the multi-group model

Asymptotic behavior of group magnetizations determined for each regime

Potential applications to social and political science modeling

Abstract

We study a multi-group version of the mean-field or Curie-Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to determine for each regime how the vector of the group magnetisations behaves asymptotically. Some possible applications to social or political sciences are discussed.