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Ising spin glasses in two dimensions: Universality and nonuniversality

P. H. Lundow¹ and I. A. Campbell²

¹Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden
²Laboratoire Charles Coulomb, Université Montpellier II, 34095 Montpellier, France

Phys. Rev. E 95, 042107 – Published 5 April, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.042107

Abstract

Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising spin glass (ISG) models in two dimensions [Lundow and Campbell, Phys. Rev. E 93, 022119 (2016)]. Here we further analyze the bimodal and Gaussian data together with data on two other continuous interaction distribution two-dimensional ISG models, the uniform and the Laplacian models, and three other discrete interaction distribution models, a diluted bimodal model, an “antidiluted” model, and a more exotic symmetric Poisson model. Comparisons between the three continuous distribution models show that not only do they share the same exponent $η \equiv 0$ but that to within the present numerical precision they share the same critical exponent $ν$ also, and so lie in a single universality class. On the other hand the critical exponents of the four discrete distribution models are not the same as those of the continuous distributions, and the present data strongly indicate that they differ from one discrete distribution model to another. This is evidence that discrete distribution ISG models in two dimensions have nonzero values of the critical exponent $η$ and do not lie in a single universality class.

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