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

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

2004-10-28

arxiv.org/abs/cond-mat/0410744v1

J. Math. Phys. 46, 063301, 2005.

Physics

Condensed Matter

Statistical Mechanics

25 pages, 4 eps figures

Scientific paper

10.1063/1.1904507

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.

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