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We present results of a theoretical study of 4He films adsorbed on graphite,based on the continuous space worm algorithm. In the first layer, we find adomain-wall phase and a (7/16) registered structure between the commensurate(1/3) and the incommensurate solid phases. For the second layer, we find onlysuperfluid and incommensurate solid phases. The commensurate phase found inprevious simulation work is only observed if first layer particles are keptfixed; it disappears upon explicitly including their zero-point fluctuations.No evidence of any "supersolid" phase is found.

Phase diagram of 4He adsorbed on graphite