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

2004/08/07 by Daniel Daboul, D. Daboul, Iksoo Chang +3 · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1140/epjb/e2004-00315-6

13 figures

arxiv created 2004/08/07 · openalex publication_date 2004/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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