Eur. Phys. J. B 41, 231-254 (2004)
https://doi.org/10.1140/epjb/e2004-00315-6

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

¹ School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
² Department of Physics, Pusan National University, Pusan 609-735, Korea

Corresponding author: ^a daboul@fractal.tau.ac.il

Received: 22 July 2004
Published online: 12 October 2004

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 are obtained to order 13 in the expansion variable 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 and for the critical exponent γ in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for γ agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.