The Ising Spin Glass in dimension five: link overlaps

TL;DR

This study uses extensive simulations to analyze the link overlap in five-dimensional Ising Spin Glasses, revealing critical maxima at the transition and complex heterogeneity in the ordered phase.

Contribution

It introduces the use of moments of link overlap distributions as efficient tools to identify freezing transitions across dimensions.

Findings

Critical maxima in kurtosis and skewness at the transition temperature.

Development of a two-peak structure in the ordered phase.

Heterogeneity in the link overlap spectra of individual samples.

Abstract

Extensive simulations are made of the link overlap in five dimensional Ising Spin Glasses (ISGs) through and below the ordering transition. Moments of the mean link overlap distributions (the kurtosis and the skewness) show clear critical maxima at the ISG ordering temperature. These criteria can be used as efficient tools to identify a freezing transition quite generally and in any dimension. In the ISG ordered phase the mean link overlap distribution develops a strong two peak structure, with the link overlap spectra of individual samples becoming very heterogeneous. There is no tendency towards a "trivial" universal single peak distribution in the range of size and temperature covered by the data.