Growth instability in helium films

We study the growth of liquid He4 films on weakly attractive substrates. Close to the substrate the film grows by formation of well defined liquid layers. Above a minimum stable coverage, a liquid monolayer uniformly covers the surface. Upon increasing the coverage a second liquid layer begins to grow by the formation of two-dimensional liquid ''clusters.'' Above a certain coverage, the second layer leaves vacuum-cluster coexistence, and the system regains the full planar symmetry. The scenario is repeated for a third liquid layer. The results are interpreted in terms of recent experiments of helium on graphite.