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Critical behavior of the Ising model on the four-dimensional cubic lattice
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2009 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 80, no 3, 031104-4 pages p.Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent alpha = 0 but a nonrigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at T(c). We find that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field-theory prediction of a logarithmic singularity is wrong.

Place, publisher, year, edition, pages
2009. Vol. 80, no 3, 031104-4 pages p.
Keyword [en]
monte-carlo
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-52120DOI: 10.1103/PhysRevE.80.031104ISI: 000270383400019OAI: oai:DiVA.org:umu-52120DiVA: diva2:497233
Note

501LM Times Cited:5 Cited References Count:18

Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2017-12-07Bibliographically approved

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Lundow, P. H.Markström, Klas
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