On the 2D Ising Wulff crystal near criticality

Annals of Probability 2010, Vol. 38, No. 1, 102-149 We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the size of t...

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Bibliographic Details
Main Authors Cerf, R, Messikh, R. J
Format Journal Article
LanguageEnglish
Published 08.03.2006
Subjects
Mathematics - Probability
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Summary:Annals of Probability 2010, Vol. 38, No. 1, 102-149 We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the size of the box grows fast enough, we establish a large deviation principle that proves the appearance of a round Wulff crystal.
Bibliography:IMS-AOP-AOP449
DOI:10.48550/arxiv.math/0603178