Kinetic Theory Approach to the SK Spin Glass Model with Glauber Dynamics

TL;DR

This paper introduces a novel kinetic theory approach, inspired by fluid dynamics, to analyze Glauber dynamics in the SK spin glass model, providing accurate predictions for spin correlations at high temperatures.

Contribution

It develops a new kinetic theory method for the SK model's Glauber dynamics, extending local equilibrium approximations and improving understanding of spin correlations.

Findings

Zeroth order theory matches simulation results at high T.

First order theory captures qualitative dynamics of correlations.

Method offers a new analytical tool for spin glass dynamics.

Abstract

I present a new method to analyze Glauber dynamics of the Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas used in the classical kinetic theory of fluids. I apply it to study spin correlations in the high temperature phase ($T\ge T_c$) of the SK model at zero external field. The zeroth order theory is equivalent to a disorder dependent local equilibrium approximation. Its predictions agree well with computer simulation results. The first order theory involves coupled evolution equations for the spin correlations and the dynamic (excess) parts of the local field distributions. It accounts qualitatively for the error made in the zeroth approximation.