Melting of a physisorbed commensurate phase

The general Landau-Ginzburg-Wilson Hamiltonian for the melting of a physisorbed $\sqrt{3}\times \sqrt{3}$ commensurate phase on a substrate of triangular lattice symmetry is examined. Two limits in which it simplifies are considered: first, the lattice-gas limit resulting from infinite substrate potential, and second, a decoupling limit in which the Hamiltonian reduces to three independent chiral clock models. Universality classes of melting transition with various degrees of symmetry might occur; evidence exists for two. It is argued that the "chiral" transition which may have been observed for Kr on graphite cannot be modeled by a simple lattice gas. Possible phase diagrams are examined and a new spin model with the appropriate symmetry is proposed. The general approach should be applicable to other commensurate surface phases.