## The Annals of Probability

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

### On the 2D Ising Wulff crystal near criticality

R. Cerf and R. J. Messikh

#### 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