Critical prewetting in the 2d Ising model

TL;DR

This paper analyzes critical prewetting phenomena in the 2D Ising model, showing that the interface between phases converges to a Ferrari-Spohn diffusion under specific scaling, revealing detailed phase transition behavior.

Contribution

It provides a rigorous analysis of the interface dynamics in the 2D Ising model with boundary conditions and external field, establishing convergence to a Ferrari-Spohn diffusion.

Findings

Interface converges to Ferrari-Spohn diffusion under scaling.

External magnetic field induces phase instability.

Detailed characterization of phase coexistence and transition.

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 $2N\times N$ 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 $\beta>\beta_{\rm c}$, 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.