Droplet growth for three-dimensional Kawasaki dynamics

The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics at low temperature and low density. Let Lambda be a large finite box subset of three-dimensional lattice. Particles perform simple exclusion on Lambda, but when they occupy neighboring sites they feel a binding energy -U<0 that slows down their dissociation. Along each bond touching the boundary of Lambda from the outside, particles are created with rate rho that is exponential of -Delta multiplied by beta and are annihilated with rate 1, where beta is the inverse temperature and Delta>0 is an activity parameter. Thus, the boundary of Lambda plays the role of an infinite gas reservoir with density rho. We consider the regime where Delta in (U,3U) and the initial configuration is such that Lambda is empty. For large beta$, the system wants to fill Lambda but is slow in doing so. We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and shape of the critical droplet\/ and the time of its creation in the limit as beta converging to infinity.