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Scientific article
English

Critical prewetting in the 2d Ising model

Published inAnnals of probability, vol. 50, no. 3, p. 1127-1172
Publication date2022
Abstract

In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N·N rectangular box with a boundary condition inducing the coexistence of the + phase in the bulk and a layer of - phase along the bottom wall. The presence of an external magnetic field of intensity h=lambda/N (for some fixed lambda>0) makes the layer of - phase unstable. For any ß>ß_c, we prove that, under a diffusing scaling by N^{-2/3} horizontally and N^{-1/3} vertically, the interface separating the layer of unstable phase from the bulk phase weakly converges to an explicit Ferrari-Spohn diffusion.

Keywords
  • Ising model
  • Ferrari-Spohn diffusion
  • Interface
  • Invariance principle
  • Critical prewetting
Citation (ISO format)
IOFFE, Dmitry et al. Critical prewetting in the 2d Ising model. In: Annals of probability, 2022, vol. 50, n° 3, p. 1127–1172. doi: 10.1214/21-AOP1555
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Identifiers
ISSN of the journal2168-894X
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