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 <Subscript> ij </Subscript>. Series for the Edwards-Anderson susceptibility <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\chi_{\mbox{}_\mathrm{EA}}$</EquationSource> </InlineEquation> are obtained to order 13 in the expansion variable (J/(k <Subscript> B </Subscript> T))<Superscript>2</Superscript> 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 <Subscript> B </Subscript> T <Subscript> c </Subscript>))<Superscript>2</Superscript> and for the critical exponent <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\gamma$</EquationSource> </InlineEquation> in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\gamma$</EquationSource> </InlineEquation> agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality. Copyright Springer-Verlag Berlin/Heidelberg 2004