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Critical prewetting in the 2d Ising model

Dmitry Ioffe, Sébastien Ott, Senya Shlosman, Yvan Velenik

24/11/20 Published in : arXiv:2011.11997

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.

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  • Statistical Mechanics

Non-analyticity of the correlation length in systems with exponentially decaying interactions

Bootstrapping Heisenberg Magnets and their Cubic Instability

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