Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model

TL;DR

This paper provides an analytical solution for the non-equilibrium dynamics of a spherical p-spin spin-glass model, revealing ergodicity breaking and aging effects in the thermodynamic limit.

Contribution

It introduces a novel analytical approach to solve the long-time dynamics of a spherical spin-glass model, including a Parisi-like order parameter for dynamics.

Findings

Demonstrates weak and true ergodicity breaking in the model.

Derives asymptotic forms of magnetization, correlation, and response functions.

Identifies a dynamic order parameter analogous to static Parisi function.

Abstract

We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N \rightarrow \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We determine a functional Parisi-like order parameter $P_d(q)$ which plays a similar role for the dynamics to that played by the usual function for the statics.