Affordable Access

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

American Physical Society
Publication Date
  • Materialer Med SæRlige Fysiske Og Kemiske Egenskaber


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.

There are no comments yet on this publication. Be the first to share your thoughts.


Seen <100 times