F. Manzo, E. Olivieri
DYNAMICAL BLUME--CAPEL MODEL: COMPETING METASTABLE STATES
AT INFINITE VOLUME
(465K, postscript)
ABSTRACT. This paper concerns the microscopic dynamical
description of competing metastable states.
We study, at infinite volume and very low temperature,
metastability and nucleation for kinetic Blume-Capel model: a ferromagnetic
lattice model with
spins taking three possible values:
$-1, 0, 1$.
In a previous paper ([MO]) we considered a simplified,
irreversible, nucleation-growth model;
in the present paper we analyze the full Blume-Capel
model.
We choose a region $U$ of the thermodynamic
parameters such that, everywhere in
$U$: $\minus $
(all minuses) corresponds to the highest (in energy)
metastable state, $\zero$ (all zeroes)
corresponds to an intermediate metastable
state and
$\plus$ (all pluses) corresponds to the stable state.
We start from
$\minus $ and look at a local observable.
Like in [MO], we find that, when crossing a special
line in $U$, 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 $-1$.