A note on the polynomial moments of the partition function in the SK model

2015/09/16 by Sergey Bocharov, Bocharov, Sergey
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1509.04780

openalex publication_date 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a simple identity relating the kth moment of the partition function Z_N(⋅) in the SK model to the Nth moment of the partition function Z_k(⋅). As a corollary we find a characterisation of the limit lim_{N → ∞} (1)/(N) log 𝔼 Z_N(β)^k alternative to the one found previously by Michel Talagrand in \cite4.

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