Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions

TL;DR

This paper investigates the correlation length in the 2D Ising spin glass with Gaussian interactions, revealing temperature-dependent behavior of the correlation length exponent and confirming scaling at low temperatures.

Contribution

It introduces an efficient Monte Carlo method enabling analysis of larger systems and lower temperatures, and demonstrates the temperature dependence of the correlation length exponent.

Findings

Correlation length exponent increases as temperature decreases

At low temperatures, the exponent approaches -1/ heta

Scaling behavior is confirmed at low temperatures

Abstract

We study the correlation length of the two-dimensional Ising spin glass with a Gaussian distribution of interactions, using an efficient Monte Carlo algorithm proposed by Houdayer, that allows larger sizes and lower temperatures to be studied than was possible before. We find that the "effective" value of the bulk correlation length exponent \nu increases as the temperature is lowered, and, at low temperatures, apparently approaches -1/\theta, where \theta ~ -0.29 is the stiffness exponent obtained at zero temperature. This means scaling is satisfied and earlier results at higher temperatures that find a smaller value for \nu are affected by corrections to scaling.