F. Manzo, E. Olivieri
RELAXATION PATTERNS FOR COMPETING METASTABLE STATES:
A NUCLEATION AND GROWTH MODEL
(72K, plainTeX)
ABSTRACT. We study, at infinite volume and very low temperature,
the relaxation mechanisms
towards stable equilibrium in presence of two competing metastable
states.
Following Dehghanpour and Schonmann we introduce a simplified
nucleation-growth
irreversible
model as an approximation for the stochastic Blume-Capel model,
a ferromagnetic lattice system with spins taking three possible
values:
$-1, 0, 1$.
Starting
from the less stable state $\minus $ (all minuses) we look at a
local observable.
We find that, when crossing a special line in the space of the
parameters, there is a change in the mechanism of transition
towards the stable
state $\plus$: we pass from a situation: \par\noindent
1) Where
the intermediate phase $\zero$ is really observable before the final
transition
with a permanence in $\zero$ typically much longer than the first
hitting time to
$\zero$; \par \noindent
to the situation: \par \noindent
2) Where $\zero$ is not observable since the typical permanence in
$\zero$ is much shorter than the
first hitting time to $\zero$ and, moreover, large growing
$0$-droplets are
almost full of $+1$ in their interior so that there are only
relatively thin
layers of zeroes between $+1$ and $-1$.