Relaxation Patterns for Competing Metastable States: a Nucleation and Growth Model
1998, v.4, Issue 4, 549-570
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 ``-'' (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 ``+'': we pass from a situation (1) where the intermediate phase ``0'' is really observable before the final transition with a permanence in ``0'' typically much longer than the first hitting time to ``0''; to the situation (2) where ``0'' is not observable since the typical permanence in ``0'' is much shorter than the first hitting time to ``0'' 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 $-1$.
Keywords: metastability,nucleation,Blume - Capel model