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Europhysics Letters (EPL)

Dynamic Simulations and Critical Exponents in Spin Glasses

L. Bernardi, Ian A. Campbell

Published Apr 10, 1994• 9 citations
Publisher

Abstract

We have used dynamic simulations to estimate certain critical exponents for spin glasses with ± J and Gaussian near-neighbour interactions in dimensions 3 and 4. The two types of system do not appear to be in the same universality class in either dimension.
DOI
10.1209/0295-5075/26/2/012

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Extensive simulations are made on Ising Spin Glasses (ISG) with Gaussian, Laplacian and bimodal interaction distributions in dimension four. Standard finite size scaling analyses near and at criticality provide estimates of the critical inverse temperatures βcβ_cβc​, critical exponents, and critical values of a number of dimensionless parameters. Independent estimates are obtained for βcβ_cβc​ and the exponent ννν from thermodynamic derivative peak data. A detailed explanation is given of scaling in the thermodynamic limit with the ISG scaling variable τ=1−β2/βc2τ= 1-β^2/β_c^2τ=1−β2/βc2​ and the appropriate scaling expressions. Data over the entire paramagnetic range of temperatures are analysed in order to obtain further estimates of the critical exponents together with correction to scaling terms. The Privman-Fisher ansatz then leads to compact scaling expressions for the whole paramagnetic regime and for all sample sizes L. Comparisons between the 4d ISG models show that the critical dimensionless parameters characteristic of a universality class, and the susceptibility and correlation length critical exponents γγγ and ννν, depend on the form of the interaction distribution. From these observations it can be deduced that critical exponents are not universal in ISGs, at least in dimension four.
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately established using a standard criterion, critical exponents and correction terms can be readily estimated by extrapolating measurements made in the thermodynamic limit regime. The data show that the critical exponents of the susceptibility γγγ and of the correlation length ννν depend on the form of the interaction distribution. This observation implies that quite generally critical exponents are not universal in ISGs.