  We study metastability and nucleation in a kinetic two-dimensional Ising
model which is driven out of equilibrium by a small random perturbation of the
usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a
nonequilibrium potential describes in a simple way metastable states and their
decay. We thus predict noise-enhanced stability of the metastable phase and
resonant propagation of domain walls at low T. This follows from the nonlinear
interplay between thermal and nonequilibrium fluctuations, which induces
reentrant behavior of the surface tension as a function of T. Our results,
which are confirmed by Monte Carlo simulations, can be also understood in terms
of a Langevin equation with competing additive and multiplicative noises.
