Monolayer Solid Helium-4 Clusters on Graphite

In order to resolve the controversy about the low density region of the phase diagram of the 4He monolayer on graphite, we have undertaken a path integral Monte Carlo study of the system. We provide direct evidence that the low density monolayer possesses solid clusters and a low density vapor as opposed to the most recent proposal that the system is in a superfluid phase. We further establish that the rounded heat capacity peaks observed at low densities are caused by melting of such solid clusters and are not associated with the suggested superfluid transition.