97-630 F. Manzo, E. Olivieri

RELAXATION PATTERNS FOR COMPETING METASTABLE STATES: A NUCLEATION AND GROWTH MODEL (72K, plainTeX) Dec 12, 97

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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 $-1$.

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