Energy gap of the bimodal two-dimensional Ising spin glass

TL;DR

This study uses an exact algorithm to analyze the energy gap and excitation degeneracies in the bimodal 2D Ising spin glass, revealing non-self-averaging specific heat behavior and explaining the energy gap in relation to correlation length.

Contribution

It introduces a method to compute degeneracies of excited states in the bimodal 2D Ising spin glass and explains the relationship between energy gap and correlation length.

Findings

Specific heat is not self-averaging at low temperatures.

Most likely value of specific heat scales as L^3 T^(-2) exp(-4J/kT).

Correlation length scales as exp(2J/kT).

Abstract

An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a distribution that is neither normal or lognormal. Nevertheless, it is possible to estimate the most likely value and this is found to scale as L^3 T^(-2) exp(-4J/kT), for a L*L lattice. Our analysis also explains, for the first time, why a correlation length \xi ~ exp(2J/kT) is consistent with an energy gap of 2J. Our method allows us to obtain results for up to 10^5 disorder realizations with L <= 64. Distributions of second and third excitations are also shown.