Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg

TL;DR

This paper presents a numerical analysis of equilibrium relaxation in the Sherrington-Kirkpatrick Ising spin glass model at and above Tg, revealing stretched exponential behavior with a temperature-dependent exponent approaching 1/3 at Tg.

Contribution

It provides detailed numerical evidence of relaxation dynamics in the SK model and compares these findings to 3D ISG results, discussing phase space percolation.

Findings

Relaxation follows a stretched exponential form.

Exponent beta(T) approaches ~ 1/3 at Tg.

Results support a phase space percolation transition scenario.

Abstract

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~ exp[-(t/tau(T))^beta(T)] with an exponent beta(T) tending to ~ 1/3 at Tg. The results are compared to those which were observed by Ogielski in the 3d ISG model, and are discussed in terms of a phase space percolation transition scenario.