  Applying a numerical transfer-matrix formalism, we obtain complex-valued
constrained free energies for the two-dimensional square-lattice
nearest-neighbor Ising ferromagnet below its critical temperature and in an
external magnetic field. In particular, we study the imaginary part of the
constrained free-energy branch that corresponds to the metastable phase.
Although droplets are not introduced explicitly, the metastable free energy is
obtained in excellent agreement with field-theoretical droplet-model
predictions. The finite-size scaling properties are different in the weak-field
and intermediate-field regimes, and we identify the corresponding different
critical-droplet shapes. For intermediate fields, we show that the surface free
energy of the critical droplet is given by a Wulff construction with the
equilibrium surface tension. We also find a prefactor exponent in complete
agreement with the field-theoretical droplet model. Our results extend the
region of validity for known results of this field-theoretical droplet model,
and they indicate that this transfer-matrix approach provides a nonperturbative
numerical continuation of the equilibrium free energy into the metastable
phase.
