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

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• Generalized canonical ensembles and ensemble equivalence
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Cited by in corpus (21)

• The large deviation approach to statistical mechanics
• 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
• Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ${\varphi }^4$ spin model
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
• Universal anomalous fluctuations in charged single-file systems
• Ensemble inequivalence in random graphs
• Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models
• Nonconcave entropies from generalized canonical ensembles
• Methods for calculating nonconcave entropies
• Fluctuations of the magnetization in the Block Potts Model
• Energy Landscape and Metastability of Curie-Weis-Potts Model
• Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line
• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models
• Metastability of the three-state Potts model with general interactions
• Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques
• Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics
• Energy landscape of the two-component Curie-Weiss-Potts model with three spins
• Color symmetry and ferromagnetism in Potts spin glass
• On Approximating the Potts Model with Contracting Glauber Dynamics