  In honor of Onsager's ninetieth birthday, we like to review some exact
results obtained so far in the chiral Potts models and to 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 shall pay special attention to the interfacial
tension $\epsilon_r$ between the $k$ state and the $k-r$ state. By examining
the ground states, it is seen that the integrable line ends at a superwetting
point, on which the relation $\epsilon_r=r\epsilon_1$ 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 non-wet 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.

Condensed Matter;High Energy Physics - Theory