Probability Theory and Related Fields

, Volume 136, Issue 4, pp 619–660

Cugliandolo-Kurchan equations for dynamics of Spin-Glasses


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: 82C31 60H10 60F15 60K35 

Key words or phrases

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

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gérard Ben Arous
    • 1
    • 2
  • Amir Dembo
    • 3
  • Alice Guionnet
    • 4
  1. 1.Courant Institute of Mathematical SciencesNew YorkUSA
  2. 2.EPFLLausanneSwitzerland
  3. 3.Department of Statistics and Department of MathematicsStanford UniversityStanfordUSA
  4. 4.UMPA, Ecole Normale Superieure de Lyon 46 allée d'ItalieLyon Cedex 07France