2004/10/28 by Marius Costeniuc, Richard S. Ellis, Hugo Touchette
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.1904507
published as J. Math. Phys. 46, 063301, 2005. · 25 pages, 4 eps figures
arxiv created 2004/10/28 · openalex publication_date 2005/05/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 nearest-neighbor Potts model. It is equivalent to the Potts model on the complete graph on n vertices. The 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.