The Annals of Probability

On the 2D Ising Wulff crystal near criticality

R. Cerf and R. J. Messikh

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Abstract

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.

Article information

Source
Ann. Probab., Volume 38, Number 1 (2010), 102-149.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1264433994

Digital Object Identifier
doi:10.1214/08-AOP449

Mathematical Reviews number (MathSciNet)
MR2599195

Zentralblatt MATH identifier
1185.82010

Subjects
Primary: 60F10: Large deviations 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Large deviations criticality phase coexistence Wulff shape Ising model

Citation

Cerf, R.; Messikh, R. J. On the 2D Ising Wulff crystal near criticality. Ann. Probab. 38 (2010), no. 1, 102--149. doi:10.1214/08-AOP449. https://projecteuclid.org/euclid.aop/1264433994


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