TY - JOUR

T1 - Numerical transfer-matrix study of a model with competing metastable states

AU - Fiig, T.

AU - Gorman, B.M.

AU - Rikvold, P.A.

AU - Novotny, M.A.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - Materialer med særlige fysiske og kemiske egenskaber

U2 - 10.1103/PhysRevE.50.1930

DO - 10.1103/PhysRevE.50.1930

M3 - Journal article

VL - 50

SP - 1930

EP - 1947

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

SN - 2470-0045

IS - 3

ER -