Critical region for droplet formation in the two-dimensional Ising model

Marek Biskup, Lincoln Chayes, and Roman Kotecky

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Submission date: 13. Dec. 2002
Pages: 49
published in: Communications in mathematical physics, 242 (2003) 1/2, p. 137-183 
DOI number (of the published article): 10.1007/s00220-003-0946-x
Bibtex
Keywords and phrases: droplet formation, ising model, wulff shape
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Abstract:
We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size , inverse temperature  and overall magnetization conditioned to take the value , where  is the critical temperature,  is the spontaneous magnetization and is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when  tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value  and a function  such that the following holds: For , there are no droplets beyond  scale, while for , there is a single, Wulff-shaped droplet containing a fraction  of the magnetization deficit and there are no other droplets beyond the scale of . Moreover,  and  are related via a universal equation that apparently is independent of the details of the system.