, Volume 136, Issue 4, pp 619-660
Date: 24 Apr 2006

Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

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Abstract

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.

Research partially supported by NSF grants #DMS-0406042, #DMS-FRG-0244323