Test of universality in the Ising spin glass using high temperature graph expansion

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 EdwardsAnderson susceptibility X_EA are obtained to order 13 in the expansion variable (J/(k_BT))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 Ml and M2, leads to estimates for the critical threshold (J/(k_BT _c))₂ and for the critical exponent 7 in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for 7 agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.