Stochastic growth of a stable phase from a metastable phase

When a stable phase is adjacent to a metastable phase with a planar interface, the stable phase grows. We propose a stochastic model describing the phase growth accompanying latent heat. The model is based on an energy-conserving Potts model with a kinetic energy term defined on a sparsely random lattice only in one direction. For this model, we calculate the stable and metastable phases exactly using statistical mechanics. Performing numerical simulations, we find that the growth law is qualitatively different from that of the deterministic phase-field model.