Critical prewetting in the 2d Ising model

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=λ/N (for some fixed λ>0) makes the layer of − phase unstable. For any β>βc, 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.

Topics & Concepts