Fluctuations of a layer of unstable phase in the planar Ising model

Abstract: I'll first review some of the known results about phase separation, fluctuations of interfaces and (equilibrium) aspects of metastability in the planar Ising model. This will naturally lead us to consider a setup in which an interface separates a layer of unstable phase along the boundary of the system from the stable phase occupying the bulk. I'll then describe a recent work, in which we prove that, after a 1/3:2/3 scaling, the distribution of this interface weakly converges to the distribution of the stationary trajectories of an explicit Ferrari-Spohn diffusion. The proof relies on a rigorous reduction to an effective interface model, which I'll briefly sketch.

This is based on a joint work with Dima Ioffe, Sébastien Ott and Senya Shlosman; arXiv:2011.11997 .

mathematical physics

Audience: researchers in the discipline

( video )

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