Abstract
Critical prewetting in the 2d Ising model
D. Ioffe, S. Ott, S. Shlosman, Y. Velenik
Annals of Probability
50,
1127-1172
(2022).
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.
Key words:
Ising model, Ferrari-Spohn diffusion, interface, invariance principle, critical prewetting
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