Cugliandolo-Kurchan equations for dynamics of spin-glasses

Gérard Ben Arous, Amir Dembo, Alice Guionnet

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)619-660
Number of pages42
JournalProbability Theory and Related Fields
Volume136
Issue number4
DOIs
StatePublished - Dec 2006

Fingerprint

Langevin Dynamics
Nonlinear Integro-differential Equations
Mean-field Model
Statistical Physics
Spin Glass
Response Function
Strong Solution
Infinity
Converge
Family

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Analysis

Cite this

Cugliandolo-Kurchan equations for dynamics of spin-glasses. / Ben Arous, Gérard; Dembo, Amir; Guionnet, Alice.

In: Probability Theory and Related Fields, Vol. 136, No. 4, 12.2006, p. 619-660.

Research output: Contribution to journalArticle

Ben Arous, Gérard ; Dembo, Amir ; Guionnet, Alice. / Cugliandolo-Kurchan equations for dynamics of spin-glasses. In: Probability Theory and Related Fields. 2006 ; Vol. 136, No. 4. pp. 619-660.
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