01-121 F. Manzo, E. Olivieri

DYNAMICAL BLUME--CAPEL MODEL: COMPETING METASTABLE STATES AT INFINITE VOLUME (465K, postscript) 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 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 $-1$.

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