Probability Theory and Related Fields

, Volume 136, Issue 4, pp 619–660

Cugliandolo-Kurchan equations for dynamics of Spin-Glasses


  • Gérard Ben Arous
    • Courant Institute of Mathematical Sciences
    • EPFL
    • Department of Statistics and Department of MathematicsStanford University
  • Alice Guionnet
    • UMPA, Ecole Normale Superieure de Lyon 46 allée d'Italie

DOI: 10.1007/s00440-005-0491-y

Cite this article as:
Ben Arous, G., Dembo, A. & Guionnet, A. Probab. Theory Relat. Fields (2006) 136: 619. doi:10.1007/s00440-005-0491-y


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: 82C3160H1060F1560K35

Key words or phrases

Interacting random processesDisordered systemsStatistical mechanicsLangevin dynamicsAgingp-spin models
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© Springer-Verlag Berlin Heidelberg 2006