Open Access
January 2010 On the 2D Ising Wulff crystal near criticality
R. Cerf, R. J. Messikh
Ann. Probab. 38(1): 102-149 (January 2010). DOI: 10.1214/08-AOP449


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.


Download Citation

R. Cerf. R. J. Messikh. "On the 2D Ising Wulff crystal near criticality." Ann. Probab. 38 (1) 102 - 149, January 2010.


Published: January 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1185.82010
MathSciNet: MR2599195
Digital Object Identifier: 10.1214/08-AOP449

Primary: 60F10 , 60K35

Keywords: Criticality , Ising model , large deviations , phase coexistence , Wulff shape

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 1 • January 2010
Back to Top