Continuity of the nucleation of bulk and surface phases

Nucleation of a new bulk phase is almost always heterogeneous: It occurs at a surface. Nucleation of a new surface phase also occurs at a surface of course. We study nucleation in an Ising model with both bulk and surface (prewetting) transitions. We find no clear distinction between nucleation of the bulk and surface phases. As the bulk transition is crossed, the phase that is nucleating changes from being a new surface phase to being a new bulk phase. However, neither the nucleation rate nor the nucleus itself changes discontinuously. It appears that because the nucleus is only approximately two spins high, it is oblivious to the fact that on one side of the bulk transition it will grow to form a thick wetting layer, while on the other side it will grow to form a bulk phase of limitless thickness. The phase diagram of hard spheres at a hard wall is analogous to that of our model. Therefore, we suggest that the nucleation of the crystal phase of hard spheres at a hard wall may also be indistinguishable from that associated with a prefreezing surface transition.