Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
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We study the Langevin dynamics for the family of spherical p-spin disordered mean-field models of statistical physics. We prove that in the limit of system size N approaching infinity, the empirical state correlation and integrated response functions for these N-dimensional coupled diffusions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations intensively studied by Cugliandolo and Kurchan.
Mathematics Subject ClassificationPrimary: 82C44 Secondary: 82C31 60H10 60F15 60K35
Key words or phrasesInteracting random processes Disordered systems Statistical mechanics Langevin dynamics Aging p-spin models
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