Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

Details Cugliandolo-Kurchan equations for dynamics of Spin-Glasses Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

2004-09-16

arxiv.org/abs/math/0409273v1

Mathematics

Probability

31 pages

Scientific paper

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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