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Strong universality and algebraic scaling in two-dimensional Ising spin glasses

T. Jorg·J. Lukic·E. Marinari·O. C. Martin
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Abstract

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $η\approx 0$ and $ν\approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.

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T. Jorg, J. Lukic, E. Marinari, O. C. Martin. 2006-10-26. Strong universality and algebraic scaling in two-dimensional Ising spin glasses. https://doi.org/10.1103/physrevlett.96.237205

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