Limit Theorems and Coexistence Probabilities for the Curie-Weiss Potts Model with an external field

TL;DR

This paper analyzes the fluctuations and coexistence probabilities in the Curie-Weiss Potts model with an external field, revealing detailed behavior across different parameter regimes including critical and extremal points.

Contribution

It provides a comprehensive description of the fluctuation behavior and coexistence probabilities for the Curie-Weiss Potts model with external field, including at critical and extremal points.

Findings

Fluctuations of the density vector are characterized across the entire parameter domain.

Probabilities of stable states on the critical line are explicitly computed.

Results extend to the Random-Cluster model on the complete graph.

Abstract

The Curie-Weiss Potts model is a mean field version of the well-known Potts model. In this model, the critical line $\beta = \beta_c (h)$ is explicitly known and corresponds to a first order transition when $q > 2$. In the present paper we describe the fluctuations of the density vector in the whole domain $\beta \geqslant 0$ and $h \geqslant 0$, including the conditional fluctuations on the critical line and the non-Gaussian fluctuations at the extremity of the critical line. The probabilities of each of the two thermodynamically stable states on the critical line are also computed. Similar results are inferred for the Random-Cluster model on the complete graph.