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We have used the Path Integral Monte Carlo method to simulate a monolayer ofmolecular hydrogen on graphite above 1/3 submonolayer coverage. We find that atlow temperature and as the coverage increases the system undergoes a series oftransformations starting from the $\sqrt{3} \times \sqrt{3}$ commensurate solidnear 1/3 coverage. First, a phase is formed which is characterized by auniaxially compressed incommensurate solid with additional mass densitymodulations along the same direction which can be viewed as an ordereddomain-wall solid with a characteristic domain-wall distance which depends onthe surface coverage. At low temperature and higher coverage there is atransition to an incommensurate solid which is rotated relative to thesubstrate commensurate lattice. As a function of temperature the domain-wallordering first melts into a fluid of domain-walls and at higher temperature thesolid melts into a uniform fluid. Regardless of the large amplitude of quantumfluctuations, these phase transitions are analogous to those in classicalmonolayer films. Our calculated values for the surface coverage and temperaturewhere these transitions occur, the calculated structure factors and specificheat are in general agreement with the available experimental results with noadjustable parameteters.Comment: 7 Revtex pages, 12 figure

Commensurate-incommensurate transitions in quantum films: Submonolayer molecular hydrogen on graphite