- 01-121 F. Manzo, E. Olivieri
- DYNAMICAL BLUME--CAPEL MODEL: COMPETING METASTABLE STATES
AT INFINITE VOLUME
Mar 30, 01
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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
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
$\plus$ (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
the intermediate phase $\zero$ is really observable before the final
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
almost full of $+1$ in their interior so that there are only
layers of zeroes between $+1$ and $-1$.