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 -