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Complete graph asymptotics for the Ising and random-cluster models on five-dimensional grids with a cyclic boundary
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, 022112Article in journal (Refereed) Published
Abstract [en]

The finite-size scaling behavior for the Ising model in five dimensions, with either free or cyclic boundary, has been the subject of a long-running debate. The older papers have been based on ideas from, e.g., field theory or renormalization. In this paper we propose a detailed and exact scaling picture for critical region of the model with cyclic boundary. Unlike the previous papers our approach is based on a comparison with the existing exact and rigorous results for the FK-random-cluster model on a complete graph. Based on those results we predict several distinct scaling regions in an L  -dependent window around the critical point. We test these predictions by comparing with data from Monte Carlo simulations and find a good agreement. The main feature which differs between the complete graph and the five-dimensional model with free boundary is the existence of a bimodal energy distribution near the critical point in the latter. This feature was found by the same authors in an earlier paper in the form of a quasi-first-order phase transition for the same Ising model.

Place, publisher, year, edition, pages
American Physical Society , 2015. Vol. 91, 022112
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:umu:diva-99987DOI: 10.1103/PhysRevE.91.022112ISI: 000349910000001OAI: oai:DiVA.org:umu-99987DiVA: diva2:789125
Available from: 2015-02-17 Created: 2015-02-17 Last updated: 2017-12-04Bibliographically approved

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Lundow, Per-HåkanMarkström, Klas
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