F.-R. Nardi, E. Olivieri, E. Scoppola.
Anisotropy effects in nucleation for conservative dynamics.
(1250K, postscript)

ABSTRACT.  We analyze metastability and nucleation in the context of  a local version
of the  
Kawasaki dynamics  for the two-dimensional {\it anisotropic} Ising lattice
gas at very low temperature.
Let $\L\subset\Z^2$ be a sufficiently large finite box. Particles perform
simple exclusion on $\L$, but when they occupy neighboring sites
they feel a binding energy $-U_1<0$ in the horizontal direction
and  $-U_2<0$ in the vertical direction. 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 take $\D\in (U_1,U_1+U_2)$ where the totally empty (full) 
configuration can be naturally associated to metastability (stability). We
investigate
how the transition from empty to full takes place under the
dynamics. In particular, we identify the size and  some
characteristics of the shape of the {\it critical droplet\/} and
the time of its creation in the limit as $\b\to\infty$.
We observe very different behavior in the weakly or strongly anisotropic
case.
In any case we find that Wulff shape is not relevant for the nucleation
pattern.