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

T. Fiig, B. M. Gorman, P. A. Rikvold, and M. A. Novotny
Phys. Rev. E 50, 1930 – Published 1 September 1994
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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 fα. For particular eigenvectors of the transfer matrix, the fα 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∝‖Imfα‖, 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

Authors & Affiliations

T. Fiig

  • Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052
  • Department of Solid State Physics, Riso/ National Laboratory, DK-4000 Roskilde, Denmark

B. M. Gorman and P. A. Rikvold

  • Supercomputer Computations Research Institute, Center for Materials Research and Technology, and Department of Physics, Florida State University, Tallahassee, Florida 32306-4052

M. A. Novotny

  • Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052

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Vol. 50, Iss. 3 — September 1994

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