Droplet Motion for the Conservative 2D Ising Lattice Gas Dynamics below the Critical Temperature

Abstract

We consider the 2D Ising lattice gas in a square of side L with free boundary conditions, temperature below the critical one and particle density slightly above the density of the vapor phase. Typical configurations consist of a quarter of a Wulff droplet of the liquid phase centered at one of the corners of the given square. We then introduced a reversible Markovian spin exchange dynamics, also known as Kawasaki dynamics, on the configuration space and we discuss the heuristics of the transition of a bubble of the liquid phase from one corner to another. We then present some numerical evidence suggesting that the preferred mechanism to make the transition is via evaporation of the original bubble and simultaneous reconstruction of a new bubble around a new corner.