Non-equilibrium dynamics of simple spherical spin models

TL;DR

This paper studies the non-equilibrium aging dynamics of spherical spin models, revealing a universal intermediate time scale where fluctuation-dissipation relations break down, with implications for understanding spin glass behavior.

Contribution

It provides an exact analysis of aging and fluctuation-dissipation violations in spherical spin models, highlighting a universal intermediate time scale separating short-time and aging regimes.

Findings

Identification of a universal intermediate time scale in aging dynamics

Demonstration of fluctuation-dissipation violation at this time scale

Comparison of aging behavior with experimental spin glass observations

Abstract

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic dynamics has for large times and for large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation regime is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like the thermoremanent magnetization.