Limiting Dynamics for Spherical Models of Spin Glasses with Magnetic Field

TL;DR

This paper analyzes the large-system limit of spherical spin glass models with magnetic fields, showing convergence of key dynamical quantities to solutions of explicit equations and deriving the fluctuation-dissipation theorem regime.

Contribution

It extends the dynamical analysis of spherical spin glasses to include magnetic fields, providing explicit equations and rigorous FDT regime derivation.

Findings

Convergence of empirical correlation, response, overlap, and magnetization to explicit equations.

Derivation of the FDT regime in a broad temperature-magnetization region.

Generalization of the Cugliandolo-Kurchan system with magnetic field.

Abstract

We study the Langevin dynamics for the family of spherical spin glass models of statistical physics, in the presence of a magnetic field. We prove that in the limit of system size N approaching infinity, the empirical state correlation, the response function, the overlap and the magnetization for these N-dimensional coupled diffusions converge to the non-random unique strong solution of four explicit non-linear integro-differential equations, that generalize the system proposed by Cugliandolo and Kurchan in the presence of a magnetic field. We then analyze the system and provide a rigorous derivation of the FDT regime in a large area of the temperature-magnetization plane.