  In simulations of the 2D Ising model, we examine heterogeneous nucleation
induced by a small impurity consisting of a line of $l$ fixed spins. As $l$
increases, we identify a limit of stability beyond which the metastable phase
is not defined. We evaluate the free energy barrier for nucleation of the
stable phase, and show that contrary to expectation, the barrier does not
vanish on approach to the limit of stability. We also demonstrate that our
values for the height of the barrier yield predictions for the nucleation time
(from transition state theory) and the size of the critical cluster (from the
nucleation theorem) that are in excellent agreement with direct measurements,
even near the limit of stability.
