Numerical transfer-matrix study of a model with competing metastable states.

Abstract

The Blume-Capel model, a three-state lattice-gas model capable of displaying competing metastable states, is investigated in the limit of weak, long-range interactions. The methods used are scalar field theory, a numerical transfer-matrix method, and dynamical Monte Carlo simulations. The equilibrium phase diagram and the spinodal surfaces are obtained by mean-field calculations. The model's Ginzburg-Landau-Wilson Hamiltonian is used to expand the free-energy cost of nucleation near the spinodal surfaces to obtain an analytic continuation of the free-energy density across the first-order phase transition. A recently developed transfer-matrix formalism is applied to the model to obtain complex-valued constrained'' free-energy densities [ital f][sub [alpha]]. For particular eigenvectors of the transfer matrix, the [ital f][sub [alpha]] exhibit finite-range scaling behavior in agreement with the analytically continued metastable free-energy density. This transfer-matrix approach gives a free-energy cost of nucleation that supports the proportionality relation for the decay rate of the metastable phase [Gamma][proportional to][vert bar]Im[ital f][sub [alpha]][vert bar], even in cases where two metastable states compete. The picture that emerges from this study is verified by Monte Carlo simulation.