Preprint 110/2002

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
Keywords and phrases: droplet formation, ising model, wulff shape
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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 formula10, inverse temperature formula12 and overall magnetization conditioned to take the value formula14, where formula16 is the critical temperature, formula18 is the spontaneous magnetization and formula20 is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when formula22 tends to a definite limit. Specifically, we identify a dimensionless parameter formula24, proportional to this limit, a non-trivial critical value  and a function formula28 such that the following holds: For formula30, there are no droplets beyond formula32 scale, while for formula34, there is a single, Wulff-shaped droplet containing a fraction formula36 of the magnetization deficit and there are no other droplets beyond the scale of formula32. Moreover, formula28 and formula24 are related via a universal equation that apparently is independent of the details of the system.

18.10.2019, 02:11