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

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 χ_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-Padé 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 γin dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for γagree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.

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