Mean Field Dynamical Exponents in Finite-Dimensional Ising Spin Glass

TL;DR

This paper measures the dynamical critical exponent in six-dimensional Ising spin glasses using multiple methods, confirming the mean field prediction, and compares remanent magnetization behavior in higher dimensions with the SK model.

Contribution

It provides numerical estimates of the dynamical exponent in finite-dimensional spin glasses and compares their behavior with mean field models.

Findings

Dynamical exponent z ≈ 4 in 6D spin glass

Good agreement with mean field predictions

Remanent magnetization behavior matches SK model in high dimensions

Abstract

We report the value of the dynamical critical exponent z for the six dimensional Ising spin glass, measured in three different ways: from the behavior of the energy and the susceptibility with the Monte Carlo time and by studying the overlap-overlap correlation function as a function of the space and time. All three results are in a very good agreement with the Mean Field prediction z=4. Finally we have studied numerically the remanent magnetization in 6 and 8 dimensions and we have compared it with the behavior observed in the SK model, that we have computed analytically.