The Critical Exponent $\theta'$ in Spin Glasses

TL;DR

This paper investigates the short-time dynamic scaling in 3D $ ext{±}J$ Ising spin glasses using Monte Carlo simulations, focusing on the critical exponent $ heta'$ and the dynamic exponent z.

Contribution

It introduces a method to measure the critical exponent $ heta'$ and estimates the dynamic exponent z in 3D Ising spin glasses through Monte Carlo simulations.

Findings

Measured the initial increase of the overlap q(t)

Estimated the critical exponent $ heta'$

Calculated the dynamic exponent z

Abstract

Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent $\theta'$ is obtained. From the scaling relation $\lambda =d/z-\theta'$, the dynamic exponent z is estimated.