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

T. Fiig, B.M. Gorman, P.A. Rikvold, M.A. Novotny

    Research output: Contribution to journalJournal articleResearch

    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 f(alpha). For particular eigenvectors of the transfer matrix, the f(alpha) exhibit finite-rangescaling 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 T proportional to\Imf alpha\, even in cases where two metastable states compete. The picture that emerges from this study is verified by Monte Carlo simulation.
    Original languageEnglish
    JournalPhysical Review E
    Volume50
    Issue number3
    Pages (from-to)1930-1947
    ISSN1063-651X
    DOIs
    Publication statusPublished - 1994

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