Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion

TL;DR

This study uses high-temperature graph expansions to analyze the universality of critical behavior in the Ising spin glass model across multiple dimensions, confirming that critical exponents are independent of the distribution of interactions.

Contribution

It provides the first detailed high-temperature expansion analysis for the Ising spin glass, confirming universality of critical exponents across different interaction distributions in various dimensions.

Findings

Critical exponents b3 are consistent across different distributions within uncertainties.

The critical threshold (J/(k_B T_c))^2 is estimated for multiple dimensions.

Universality of critical behavior is confirmed in dimensions 4, 5, 7, and 8.

Abstract

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for the general d-dimensional hyper-cubic lattice, where the parameter J determines the width of the distributions. We explain in detail how the expansions are calculated. The analysis, using the Dlog-Pad\'e approximation and the techniques known as M1 and M2, leads to estimates for the critical threshold (J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for \gamma agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.