  We investigate heterogeneous and homogeneous nucleation in nearest-neighbor
and long-range Ising models for various quench depths. We find that the system
has a true crossover from heterogeneous to homogeneous nucleation for
increasing quench depth only if the interaction is sufficiently long-range. The
survival curves, defined as the fraction of systems that remain in the
metastable state after a given time, have qualitatively different shapes as a
function of quench depth for heterogeneous and homogeneous nucleation when the
interaction is short-range, but have identical shapes within the accuracy of
our data for long-range interactions.
