High-Temperature Dynamics of Spin Glasses

TL;DR

This paper introduces a high-temperature expansion method to analyze the non-equilibrium dynamics of spin glasses, providing theoretical predictions that align well with Monte Carlo simulations.

Contribution

It presents a systematic high-temperature expansion approach for the SK and finite-dimensional $ ext{±}J$ spin glass models in non-equilibrium states, improving understanding of their dynamics.

Findings

Theoretical curves agree with Monte Carlo results in relevant temperature and time ranges.

Derived dynamical probability distribution function from the master equation.

Comparison with existing theories highlights the method's effectiveness.

Abstract

We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master equation using a high temperature expansion. We calculate the expectation values of physical quantities from the dynamical probability distribution function. The theoretical curves show satisfactory agreement with Monte Carlo simulation results in the appropriate temperature and time regions. A comparison is made with the results of a dynamics theory by Coolen, Laughton and Sherrington.