Dynamical Blume–Capel Model: Competing Metastable States at Infinite Volume

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: −\b{1} (all minuses) corresponds to the highest (in energy) metastable state, \b{0} (all zeroes) corresponds to an intermediate metastable state and +\b{1} (all pluses) corresponds to the stable state. We start from −\b{1} 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 +\b{1}. We pass from a situation: 1. where the intermediate phase \b{0} is really observable before the final transition, with a permanence in \b{0} typically much longer than the first hitting time to \b{0}; to the situation: 2. where \b{0} is not observable since the typical permanence in \b{0} is much shorter than the first hitting time to \b{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.