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Hyperscaling Violation in Ising Spin Glasses
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 10, article id 978Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MDPI, 2019. Vol. 21, no 10, article id 978
Keywords [en]
spin glasses, random interactions, scaling, hyperscaling
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-165329DOI: 10.3390/e21100978ISI: 000495094000060OAI: oai:DiVA.org:umu-165329DiVA, id: diva2:1374572
Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2019-12-02Bibliographically approved

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Lundow, Per-Håkan
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