Series Expansion of the Off-Equilibrium Mode Coupling Equations

TL;DR

This paper introduces a series expansion method for analyzing off-equilibrium mode coupling equations, providing insights into the long-term behavior of disordered systems, specifically applied to the spherical spin glass model.

Contribution

It develops a Taylor expansion approach to solve off-equilibrium dynamical equations, enabling detailed analysis of asymptotic energy and decay coefficients in spin glasses.

Findings

Computed asymptotic energy in the critical region and at zero temperature.

Determined coefficients of the energy decay over time.

Validated the effectiveness of series expansion for long-time dynamics.

Abstract

We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior. We study the $p=3$ spherical spin glass model, and we compute the asymptotic energy (in the critical region and down to $T=0$) and the coefficients of the time decay of the energy.