Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model

TL;DR

This paper rigorously analyzes phase transitions and ensemble equivalence in the Curie-Weiss-Potts model using large deviations, providing explicit formulas and insights into microcanonical and canonical ensembles.

Contribution

It offers the first detailed and rigorous analysis of phase transitions and ensemble equivalence for the Curie-Weiss-Potts model, including explicit formulas for entropy and macrostates.

Findings

Explicit formulas for microcanonical entropy and equilibrium macrostates.

Analysis of ensemble equivalence and nonequivalence based on entropy properties.

Identification of phase transition structures in the model.

Abstract

Using the theory of large deviations, we analyze the phase transition structure of the Curie-Weiss-Potts spin model, which is a mean-field approximation to the Potts model. This analysis is carried out both for the canonical ensemble and the microcanonical ensemble. Besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles, we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates, relating these to concavity and support properties of the microcanonical entropy. The Curie-Weiss-Potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out.