Journal article
Numerical transfer-matrix study of a model with competing metastable states
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.
Language: | English |
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Year: | 1994 |
Pages: | 1930-1947 |
ISSN: | 24700053 , 24700045 , 1063651x and 10953787 |
Types: | Journal article |
DOI: | 10.1103/PhysRevE.50.1930 |