THE EXACT FIELD THEORY OF PHASE SEPARATION: A JOURNEY STARTED WITH THE ISING MODEL

Alessio Squarcini (Personal webpage)

Innsbruck University, Innsbruck, Austria

In this lecture we illustrate how to employ field-theoretical methods to determine exact results for interfacial phenomena in two-dimensional systems of classical statistical mechanics. Afer a historical detour on mathemaGcal descriptions of phase coexistence and capillary fluctuations, we turn to the two-dimensional case, focusing on the important role played by the Ising model in the context of exact solutions. Subsequently, we discuss conceptual and theoretical challenges posed by models belonging to other universality classes and show how to tackle them within a unified language provided by field theory. The lecture presents results about wetting transitions and correlations at phase separation in various 2D geometries encompassing strips, half-plane and wedges.