MARK KAC SEMINAR

The Widom-Rowlinson model is one of the few models of interacting particles in the continuum for which a proof of ``liquid-vapour’’ coexistence has been provided. I will first introduce the WR model and review the proof of the phase coexistence. Then, I will turn to the phenomenon of metastability and related problems of liquid-vapour interface. After formulating the main results (the main feature is the nonstandard entropic correction to the Arrhenius law), I will pass to the main ideas of the proofs. Based on a series of papers (in arXiv or in progress), joint with Frank den Hollander, Sabine Jansen, and Elena Pulvirenti.

We prove that a metastable two-dimensional Ising model evolving at subcritical temperature in a finite but diverging box exhibits a transition from metastability to equilibrium at an asymptotically exponential timein the limit of vanishing magnetic field. We establish this result by following a pathwise approach combined with the introduction of soft-measures. We use the basics of the Wulff construction to prove that local relaxation times are short with respect to typical exit times from the basins of attraction of metastable and stable equilibria. Getting such an upper bound on local relaxation times is the key point of the proof and is based on a random path estimate inspired from block dynamics to control spectral gaps.