Three Dimensional Edwards-Anderson Spin Glass Model in an External Field

TL;DR

This study investigates the three-dimensional Edwards-Anderson spin glass model under an external field, employing GPU-accelerated Monte Carlo simulations and a novel susceptibility ratio indicator to detect phase transitions.

Contribution

It introduces a GPU-accelerated simulation approach and evaluates a new susceptibility ratio indicator for identifying spin glass phase transitions under external fields.

Findings

Conventional indicators do not show a transition at low temperatures.

The susceptibility ratio indicator exhibits crossing behavior suggestive of a transition.

Large sample sizes are necessary due to the noise in the new indicator.

Abstract

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite wavenumbers, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speedup the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities do show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This calls for a more thorough study of the three-dimension Edwards-Anderson model in an external field.