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Open AccessArticle

Hyperscaling Violation in Ising Spin Glasses

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Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, 34095 Montpellier, France
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Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden
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Author to whom correspondence should be addressed.
Entropy 2019, 21(10), 978; https://doi.org/10.3390/e21100978
Received: 12 September 2019 / Revised: 4 October 2019 / Accepted: 7 October 2019 / Published: 8 October 2019
In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models. View Full-Text
Keywords: spin glasses; random interactions; scaling; hyperscaling spin glasses; random interactions; scaling; hyperscaling
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Campbell, I.A.; Lundow, P.H. Hyperscaling Violation in Ising Spin Glasses. Entropy 2019, 21, 978.

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