Simple spin models with non-concave entropies

2005/04/30 by Hugo Touchette · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1119/1.2794350

published as Am. J. Phys. 76, 26-30, 2008 · v1: 11 pages, 5 figures. v2: Short, published version of v1, 6 pages, 3 figures. See v1 for the solutions of some of the problems listed in v2

openalex publication_date 2007/12/12 · arxiv created 2008/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. The two models are simple variations of the classical paramagnetic spin model of non-interacting spins and are solved as easily as the latter model.

Citations

• Generalized canonical ensembles and ensemble equivalence
• Complete analysis of phase transitions and ensemble equivalence for the Curie–Weiss–Potts model
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume–Emery–Griffiths model
• An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles

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