Correlation length of the two-dimensional Ising spin glass with bimodal interactions

TL;DR

This paper investigates the correlation length in a 2D Ising spin glass with bimodal interactions, finding it grows exponentially with inverse temperature, indicating a finite energy gap between ground and excited states.

Contribution

It combines advanced Monte Carlo methods to analyze the correlation length, providing evidence for an energy gap in the 2D bimodal Ising spin glass.

Findings

Correlation length grows exponentially with inverse temperature (~ exp(2J/T))

Ground state is separated from first excited state by an energy gap ~4J

Supports hyperscaling hypothesis in the system

Abstract

We study the correlation length of the two-dimensional Edwards-Anderson Ising spin glass with bimodal interactions using a combination of parallel tempering Monte Carlo and a rejection-free cluster algorithm in order to speed up equilibration. Our results show that the correlation length grows ~ exp(2J/T) suggesting through hyperscaling that the degenerate ground state is separated from the first excited state by an energy gap ~4J, as would naively be expected.