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

25 pages, 4 eps figures

References in corpus (4)

• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Generalized canonical ensembles and ensemble equivalence
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model

Cited by in corpus (4)

• Generalized canonical ensembles and ensemble equivalence
• The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
• Mean-field driven first-order phase transitions in systems with long-range interactions
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model