  We apply a generalized numerical transfer-matrix method to the 2-d Ising
ferro- magnet 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-theoretic 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, aniso- tropic zero-field surface tension, and we present strong
evidence for Gold- stone modes on the critical cluster surface. Our results are
also fully con- sistent with average metastable lifetimes from previous
Monte-Carlo simula- tions. The study indicates that our
constrained-transfer-matrix technique pro- vides a nonperturbative numerical
method to obtain an analytic continuation of the free energy around the
essential singularity at the first-order transition.
