  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.
