A central limit theorem for a localized version of the SK model

2006/09/27 by Sérgio de Carvalho Bezerra, Bezerra, Sergio De Carvalho, Samy Tindel +1
Mathematics · Physics and Astronomy · #60K35 #82B44 #82D30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0609754

openalex publication_date 2006/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider a SK (Sherrington--Kirkpatrick)-type model on Z^d for d greater or equal to 1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit, we investigate the equivalence of this model with the usual SK spin system, through the study of the fluctuations of the free energy.

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