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 $2\mathit{N}\times \mathit{N}$ 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 $\mathit{h}=\mathit{\lambda }/\mathit{N}$ (for some fixed $\mathit{\lambda }>0$) makes the layer of − phase unstable. For any $\mathit{\beta }>{\mathit{\beta }}_{\mathrm{c}}$, we prove that, under a diffusing scaling by ${\mathit{N}}^{-2/3}$ horizontally and ${\mathit{N}}^{-1/3}$ vertically, the interface separating the layer of unstable phase from the bulk phase weakly converges to an explicit Ferrari–Spohn diffusion.