We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous nucleation and growth in kinetic Ising and lattice-gas models. An introductory discussion of the droplet theory of homogeneous nucleation is followed by a discussion of Monte Carlo and transfer-matrix methods commonly used for numerical study of metastable decay, including some new algorithms. Next we discuss specific classes of systems. These include a brief discussion of recent progress for fluids, and more exhaustive considerations of ferromagnetic Ising models (i.e., attractive lattice-gas models) with weak long-range interactions and with short-range interactions. Whereas weak-long-range-force (WLRF) models have infinitely long-lived metastable phases in the infinite-range limit, metastable phases in short-range-force (SRF) models eventually decay, albeit extremely slowly. Recent results on the finitesize scaling of metastable lifetimes in SRF models are reviewed, and it is pointed out that such effects may be experimentally observable.

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 ×∞ quasi-one-dimensional Ising model. Using the field theory, we find the analytic continuationf 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 EulerLagrange equation for the model numerically, we have verified the form of the free-energy cost of nucleation, including the first correction. In the transfermatrix method we associate with subdominant eigenvectors of the transfer matrix a complex-valued "constrained" free-energy density f α computed directly from the matrix. For the eigenvector with an associated magnetization most strongly opposed to the applied magnetic field, f α exhibits finite-range scaling behavior in agreement withf 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.

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