Abstract
The specific heat of a two-layer $^{4}\mathrm{He}$ 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 [S. Nakamura, K. Matsui, T. Matsui, and H. Fukuyama, Phys. Rev. B 94, 180501(R) (2016)] 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.
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