CRITICAL PREWETTING IN THE 2D ISING MODEL

• 成果类型: Article
• 署名作者: Ioffe, Dmitry; Ott, Sebastien; Shlosman, Senya; Velenik, Yvan
• 署名单位: Technion Israel Institute of Technology; Roma Tre University; University of Geneva
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1555
• 发表日期: 2022
• 页码: 1127-1172
• 关键词: surface-tension; potts; interfaces; BEHAVIOR; ferrari; limit

摘要

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 x 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 beta > beta(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.