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We apply both a scalar field theory and a recently developed transfer-matrixmethod to study the stationary properties of metastability in a two-state modelwith weak, long-range interactions: the $N$$\times$$\infty$quasi-one-dimensional Ising model. Using the field theory, we find the analyticcontinuation $\tilde f$ of the free energy across the first-order transition,assuming that the system escapes the metastable state by nucleation ofnoninteracting droplets. We find that corrections to the field-dependence aresubstantial, and by solving the Euler-Lagrange equation for the modelnumerically, we have verified the form of the free-energy cost of nucleation,including the first correction. In the transfer-matrix method we associate withsubdominant eigenvectors of the transfer matrix a complex-valued``constrained'' free-energy density $f_\alpha$ computed directly from thematrix. For the eigenvector with an associated magnetization most stronglyopposed to the applied magnetic field, $f_\alpha$ exhibits finite-range scalingbehavior in agreement with $\tilde f$ over a wide range of temperatures andfields, extending nearly to the classical spinodal. Some implications of theseresults for numerical studies of metastability are discussed.Comment: 25 pages, REVTeX, 9 figures available upon request, FSU-SCRI-93-153,  accepted for publication in Phys. Rev.

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