Numerical transfer-matrix study of metastability in the d=2 Ising model.

We apply a generalized numerical transfer-matrix method to the two-dimensional Ising ferromagnet in a nonzero field to obtain complex constrained free energies. Below T c certain eigenstates of the transfer matrix are identified as representing a metastable phase. The imaginary parts of the metastable constrained free energies are found to agree with a field-theoretical droplet model for a wide range of fields, allowing us to numerically estimate the average free-energy cost of a critical cluster. We find excellent agreement with the equilibrium cluster free energy obtained by a Wulff construction with the exact, anisotropic zero-field surface tension, and we present strong evidence for Goldstone modes on the critical cluster surface. Our results are also fully consistent with average metastable lifetimes from previous Monte Carlo simulations. The study indicates that our constrained-transfer-matrix technique provides a nonperturbative numerical method to obtain an analytic continuation of the free energy around the essential singularity at the first-order transition.