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 $Lambdasubseteq{mathbb Z}^3$ be a large finite box. 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 $rho=e^{-Deltabeta}$ and are annihilated with rate 1, where $beta$ is the inverse temperature and $D>0$ 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 $Deltain (U,3U)$ 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 $betatoinfty$. Received: 23 February 2002 / Revised version: 24 June 2002 / Published online: 24 October 2002 Mathematics Subject Classification (2000): 60K35, 82B43, 82C43, 82C80 Key words or phrases: Lattice gas – Kawasaki dynamics – Metastability – Critical droplet – Large deviations – Discrete isoperimetric inequalities