Path integral Monte Carlo simulation of the second layer of helium-4   adsorbed on graphite
  We have developed a path integral Monte Carlo method for simulating helium films and apply it to the second layer of helium adsorbed on graphite. We use helium-helium and helium-graphite interactions that are found from potentials which realistically describe the interatomic interactions. The Monte Carlo sampling is over both particle positions and permutations of particle labels.   From the particle configurations and static structure factor calculations, we find that this layer possesses, in order of increasing density, a superfluid liquid phase, a sqrt(7) x sqrt(7) commensurate solid phase that is registered with respect to the first layer, and an incommensurate solid phases. By applying the Maxwell construction to the dependence of the low-temperature total energy on the coverage, we are able to identify coexistence regions between the phases. From these, we deduce an effectively zero-temperature phase diagram. Our phase boundaries are in agreement with heat capacity and torsional oscillator measurements, and demonstrate that the experimentally observed disruption of the superfluid phase is caused by the growth of the commensurate phase. We further observe that the superfluid phase has a transition temperature consistent with the two-dimensional value. Promotion to the third layer occurs for densities above 0.212 atom/A^2, in good agreement with experiment. Finally, we calculate the specific heat for each phase and obtain peaks at temperatures in general agreement with experiment. 
Marlon Pierce and Efstratios Manousakis