Spin glass dynamics in the spherical model

Abstract

A phenomenological Langevin-like equation for spin glass dynamics is proposed and solved. The equation reproduces the static spherical model results for spin glass in the long time limit. The magnetisation, order parameter and on-site correlations are found to decay exponentially above the transition temperature and algebraically at and below it, as t to infinity . A closed-form expression for the dynamic susceptibility valid at all temperatures is also obtained.