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.

In 1949, L. Onsager proposed a statistical theory for a system of elongated molecules interacting via repulsive short-range forces. Onsager's theory predicted the existence at intermediate densities of a nematic liquid crystal phase, in which the distribution of orientations of the particles is anisotropic, while the distribution of the particles in space is homogeneous and does not exhibit the periodic variation of densities that characterizes solid crystals (periodicity in all space dimensions). I will introduce a simplified model for this problem consisting of long rods (in two dimensions) and anisotropic plates (in three dimensions), characterized by purely hard core interactions and a finite number of allowed orientations. For this model I will review some results/conjectures. This is a joint work with A. Giuliani and I. Jauslin