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Specific heat of thin $^4$He films on graphite

The specific heat of a two-layer He-4 film adsorbed on a graphite substrate is estimated as a function of temperature by Quantum Monte Carlo simulations. The results are consistent with recent experimental observations, in that they broadly reproduce their most important features. However, neither the "supersolid" nor the "superfluid hexatic" phases, of which experimental data are claimed to be evidence, are observed. It is contended that heat capacity measurements alone may not be a good predictor of structural and superfluid transitions in this system, as their interpretation is often ambiguous.