Phase diagrams of surface structures from Bethe-ansatz solutions of the quantum sine-Gordon model

Phase diagrams of uniaxial two-dimensional systems with commensurate, incommensurate, and liquid phases are derived by combining exact results for the quantum sine-Gordon model with the Kosterlitz-Thouless theory of melting. The phase diagram depends on the order of commensurability, $p$. In particular, for $p=3\mathrm{}$ (the "chiral Potts" case), we conjecture that the phase diagram contains no Lifshitz point, in contrast to previous authors; for $p=1\mathrm{}$, dislocations remove the original $\mathrm{CI}$ transition completely.