  We investigate the nucleation dynamics of the three-dimensional random field
Ising model (RFIM) under an external field. We use umbrella sampling to compute
the free-energy cost of a critical nucleus, and use forward flux sampling for
the direct estimation of nucleation rates. For moderate to strong disorder, our
results indicate that the size of the nucleating cluster is not a good reaction
coordinate, contrary to the pure Ising model. We rectify this problem by
introducing a coordinate that also accounts for the location of the nucleus.
Using the free energy barrier to predict the nucleation rate, we find
reasonable agreement, although deviations become stronger as disorder
increases. We attribute this effect to cluster shape fluctuations. We also
discuss finite-size effects on the nucleation rate.
