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

D. Daboul, Iksoo Chang, Amnon Aharony A

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants Jij. Series for the Edwards-Anderson susceptibility χ are obtained to order 13 in the expansion variable (J/(kBT)) EA 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/(kBTc)) 2 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. PACS: 05.70.Jk Critical point phenomena – 75.10.Nr Spin-glass and other random models 1We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants Jij. Series for the Edwards-Anderson susceptibility χ are obtained to order 13 in the expansion variable (J/(kBT)) EA 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/(kBTc)) 2 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. PACS: 05.70.Jk Critical point phenomena – 75.10.Nr Spin-glass and other random models 1

Jan 1, 200415 citations

Universality in short-range Ising spin glasses

E. Nogueira, S. Coutinho, Fernando Dantas Nobre +1 more

arXiv:cond-mat/9906121Physica A Statistical Mechanics and its ApplicationsSep 1, 199916 citations

High-temperature series expansion for spin glasses. I. Derivation of the series

Rajiv R. P. Singh, Sudip Chakravarty

It is shown that the free energy and the Edwards-Anderson susceptibility for Ising spin glasses have a star-graph expansion. With the use of this, a method for generating the high-temperature series for these quantities is described. The scope and the applicability of this method to other properties involving quenched disorder is discussed.

Physical review. B, Condensed matterJul 1, 198735 citations

Short-range Ising spin glasses: a critical exponent study

E. Nogueira, S. Coutinho, Fernando Dantas Nobre +1 more

arXiv:cond-mat/9809264Physica A Statistical Mechanics and its ApplicationsAug 1, 19986 citations

Low temperature behavior of the two-dimensional Ising spin glass

L. W. Lee, Helmut G. Katzgraber, A. P. Young

APSMar 1, 20040 citations

Critical exponents for Ising spin glasses through high-temperature series analysis

Rajiv R. P. Singh, Sudip Chakravarty

We present estimates of the critical exponents ν and η for the three-dimensional ±J distribution Ising spin glass based on high-temperature series analysis. The method of star graph expansion is used to obtain the series for two different susceptibilities to order W17 (W=tanh2 J/kT). The series are analyzed through first-order inhomogeneous differential approximants. Assuming Tc =1.175, we find the exponents to be ν=1.3±0.2 and η=−0.25±0.2.

Journal of Applied PhysicsApr 15, 19875 citations

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

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

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