Dynamic critical behaviour in Ising spin glasses

TL;DR

This study numerically investigates the critical dynamics of Ising spin glasses across different interaction distributions and dimensions, revealing that key dynamic exponents and ratios vary significantly with the type of distribution.

Contribution

It provides the first systematic numerical analysis showing how critical dynamic exponents depend on the interaction distribution in Ising spin glasses.

Findings

Critical dynamic exponent $z_c$ varies with interaction distribution.

Non-equilibrium autocorrelation decay exponent $\lambda_c/z_c$ depends on distribution.

Critical fluctuation-dissipation ratio $X_\infty$ changes systematically with distribution.

Abstract

The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm c}$, the non-equilibrium autocorrelation decay exponent $\lambda_c/z_{\rm c}$, and the critical fluctuation-dissipation ratio $X_{\infty}$ all vary strongly and systematically with the form of the interaction distribution.