Ordering temperatures of Ising Spin Glasses

TL;DR

This paper investigates how the ordering temperature of high-dimensional Ising Spin Glasses depends on the kurtosis of the interaction distribution, revealing a linear relation in the high dimension limit and comparing various estimation methods.

Contribution

It demonstrates that in high dimensions, the ordering temperature linearly relates to kurtosis, extending understanding of spin glass behavior across dimensions.

Findings

Ordering temperature drops linearly with kurtosis in high dimensions.

High temperature series data agree with the linear relation.

Kurtosis remains a useful ranking parameter for systems at lower dimensions.

Abstract

Exploiting an approach due to Singh and Fisher I show that in the high dimension limit the ordering temperature of near neighbour Ising Spin Glasses drops linearly with the kurtosis of the interaction distribution, in excellent agreement with accurate high temperature series data of Daboul, Chang and Aharony. At lower dimensions the linear relation no longer applies strictly but the kurtosis can still be taken to be an appropriate parameter for ranking different systems. I also compare the series estimates with simulation and Migdal-Kadanoff estimates where these are available.