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Communications in Mathematical Physics

, Volume 242, Issue 1–2, pp 137–183 | Cite as

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

  • Marek Biskup
  • Lincoln Chayes
  • Roman Kotecký
Article

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 L 2 , inverse temperature β>β c and overall magnetization conditioned to take the value m L 2 −2m v L , where β c −1 is the critical temperature, m =m (β) is the spontaneous magnetization and v L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v L 3/2 L −2 tends to a definite limit. Specifically, we identify a dimensionless parameter Δ, proportional to this limit, a non-trivial critical value Δ c and a function λΔ such that the following holds: For Δ<Δ c , there are no droplets beyond log L scale, while for Δ>Δ c , there is a single, Wulff-shaped droplet containing a fraction λΔ≥λ c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, λΔ and Δ are related via a universal equation that apparently is independent of the details of the system.

Keywords

Critical Temperature Dimensionless Parameter Critical Region Ising Model Inverse Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marek Biskup
    • 1
  • Lincoln Chayes
    • 1
  • Roman Kotecký
    • 2
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Center for Theoretical StudyCharles UniversityPragueCzech Republic

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