Probability Theory and Related Fields

, Volume 136, Issue 4, pp 619-660

First online:

Cugliandolo-Kurchan equations for dynamics of Spin-Glasses

  • Gérard Ben ArousAffiliated withCourant Institute of Mathematical SciencesEPFL
  • , Amir DemboAffiliated withDepartment of Statistics and Department of Mathematics, Stanford University Email author 
  • , Alice GuionnetAffiliated withUMPA, Ecole Normale Superieure de Lyon 46 allée d'Italie

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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 Classification

Primary: 82C44 Secondary: 82C31 60H10 60F15 60K35

Key words or phrases

Interacting random processes Disordered systems Statistical mechanics Langevin dynamics Aging p-spin models