Ensemble Inequivalence and the Spin-Glass Transition

Abstract

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.

19 pages, 7 figures

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• 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
• Random-energy model in random fields

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• Statistical Mechanical Formulation and Simulation of Prime Factorization of Integers