Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

2004/09/16 by Gerard Ben Arous, Arous, Gerard Ben, Amir Dembo +3 · 1 citation
Mathematics · Physics and Astronomy · #82C44 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:82C44

paper · pdf · doi:10.48550/arxiv.math/0409273

31 pages

arxiv created 2004/09/16 · arxiv updated 2009/12/01

Abstract

We study the Langevin dynamics for the family of spherical p-spin disordered mean-field models and prove that in the limit of system size N approaching infinity, the empirical state correlation and integrated response functions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations introduced by Cugliandolo and Kurchan.

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