The chiral Potts models revisited

We review some exact results obtained so far in the chiral Potts models and translate these results into language more transparent to physicists, so that experts in Monte Carlo calculations, high- and low-temperature expansions, and various other methods can use them. We pay special attention to the interfacial tension _r between thek state and thek-r state. By examining the ground states, it is seen that the integrable line ends at a superwetting point, on which the relation _r =r ₁ is satisfied, so that it is energetically neutral to have one interface or more. We present also some partial results on the meaning of the integrable line for low temperatures, where it lives in the nonwet regime. We make Baxter's exact results more explicit for the symmetric case. By performing a Bethe Ansatz calculation with open boundary conditions we confirm a dilogarithm identity for the low-temperature expansion which may be new. We propose a new model for numerical studies. This model has only two variables and exhibits commensurate and incommensurate phase transitions and wetting transitions near zero temperature. It appears to be not integrable, except at one point, and at each temperature there is a point where it is almost identical with the integrable chiral Potts model.