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

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

2004-08-07

arxiv.org/abs/cond-mat/0408167v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 figures

Scientific paper

10.1140/epjb/e2004-00315-6

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.

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