2011/02/28 by Zsolt Bertalan, Hidetoshi Nishimori, Hidethoshi Nishimori
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Canonical ensemble #Complex Systems and Time Series Analysis #Condensed matter physics #Ferromagnetism #Gaussian #Grand canonical ensemble #Mathematics #Microcanonical ensemble #Monte Carlo method #Phase transition #Physics #Quantum mechanics #Spin glass #Statistical Mechanics and Entropy #Statistical ensemble #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1080/14786435.2011.568018
published as Philosophical Magazine 92 (2012) 2 · 15 pages, 5 figures
arxiv created 2011/03/01 · openalex publication_date 2011/04/12 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the p-spin model with Gaussian-distributed random interactions in the microcanonical ensemble using the replica theory. For p = 2, there are only second-order phase transitions and we recover the results of Sherrington and Kirkpatrick obtained in the canonical ensemble. For p ≥ 3, the transition between the ferromagnetic and paramagnetic phases is of first order, and the microcanonical and canonical ensembles give different results. We also discuss the ensemble inequivalence of the random energy model, corresponding to the limit p → ∞. This is the first systematic treatment of spin glasses with long-range interactions in the microcanonical ensemble, which shows how the two ensembles give different results.