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 . For particular eigenvectors of the transfer matrix, the 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 Γ∝‖Im‖, even in cases where two metastable states compete. The picture that emerges from this study is verified by Monte Carlo simulation.
- Received 17 December 1993
DOI:https://doi.org/10.1103/PhysRevE.50.1930
©1994 American Physical Society