Cugliandolo-Kurchan equations for dynamics of spin-glasses

Gérard Ben Arous; Amir Dembo; Alice Guionnet

doi:10.1007/s00440-005-0491-y

Cugliandolo-Kurchan equations for dynamics of spin-glasses

Gérard Ben Arous, Amir Dembo, Alice Guionnet

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	619-660
Number of pages	42
Journal	Probability Theory and Related Fields
Volume	136
Issue number	4
DOIs	https://doi.org/10.1007/s00440-005-0491-y
State	Published - Dec 2006

Keywords

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

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-005-0491-y

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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.",

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N2 - 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.

AB - 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.

KW - Aging

KW - Disordered systems

KW - Interacting random processes

KW - Langevin dynamics

KW - Statistical mechanics

KW - p-spin models

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Cugliandolo-Kurchan equations for dynamics of spin-glasses

Abstract

Keywords

ASJC Scopus subject areas

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