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Non-vanishing boundary effects and quasi-first-order phase transitions in high dimensional Ising models
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Nuclear Physics B, ISSN 0550-3213, Vol. 845, no 1, 120-139 p.Article in journal (Refereed) Published
Abstract [en]

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d = 1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -partial derivative(2)S/partial derivative U(2). In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi-first-order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2011. Vol. 845, no 1, 120-139 p.
Keyword [en]
ising model, phase transitions, boundary effects, lattice, field
National Category
Physical Sciences
URN: urn:nbn:se:umu:diva-52105DOI: 10.1016/J.Nuclphysb.2010.12.002ISI: 000287002300005OAI: diva2:496886
Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2015-08-31Bibliographically approved

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Lundow, P. H.Markström, Klas
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Department of Mathematics and Mathematical Statistics
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