Finite-range-scaling analysis of metastability in an Ising model with long-range interactions

Abstract

We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional Ising model. Using the field theory, we find the analytic continuation $\tilde{f}$ of the free energy across the first-order transition, assuming that the system escapes the metastable state by nucleation of noninteracting droplets. We find that corrections to the field-dependence are substantial, and by solving the Euler-Lagrange equation for the model numerically, we have verified the form of the free-energy cost of nucleation, including the first correction. In the transfer-matrix method we associate with subdominant eigenvectors of the transfer matrix a complex-valued ``constrained'' free-energy density $f_{\alpha }$ computed directly from the matrix. For the eigenvector with an associated magnetization most strongly opposed to the applied magnetic field, $f_{\alpha }$ exhibits finite-range scaling behavior in agreement with $\tilde{f}$ over a wide range of temperatures and fields, extending nearly to the classical spinodal. Some implications of these results for numerical studies of metastability are discussed.

25 pages, REVTeX, 9 figures available upon request, FSU-SCRI-93-153, accepted for publication in Phys. Rev. E

References in corpus (1)

• Numerical Transfer-Matrix Study of Metastability in the d=2 Ising Model

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