den Hollander F., Nardi F.R., Olivieri E., Scoppola E.
Droplet growth for three-dimensional Kawasaki dynamics
(5511K, LaTeX2e, PostScript figures)
ABSTRACT. 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 $\L\subseteq\Z^3$ be a large finite box. Particles perform
simple exclusion on $\L$, 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 $\L$ from
the outside, particles are created with rate $\rho=e^{-\D\b}$ and
are annihilated with rate 1, where $\b$ is the inverse temperature
and $\D>0$ is an activity parameter. Thus, the boundary of $\L$
plays the role of an infinite gas reservoir with density $\rho$.
We consider the regime where $\D\in (U,3U)$ and the initial
configuration is such that $\L$ is empty. For large $\b$, the
system wants to fill $\L$ 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 $\b\to\infty$.