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Ioffe, Dmitry; Ott, Sébastien; Shlosman, Senya; Velenik, Yvan

Critical prewetting in the 2d Ising model. (English) Zbl 1502.60156

Ann. Probab. 50, No. 3, 1127-1172 (2022).
Summary: 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 \(\beta >{\beta_{\text{c}}} \), 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.

Cited in 9 Documents

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics

Keywords:

critical prewetting; Ferrari-Spohn diffusion; interface; invariance principle; Ising model; Ferrari-Spohn diffusion
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References:

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