The Chiral Potts Models Revisited

TL;DR

This paper reviews exact results in the chiral Potts models, clarifies their physical implications, and introduces a new simplified model for numerical studies of phase transitions and wetting phenomena.

Contribution

It translates complex mathematical results into accessible language, explores the integrable line and wetting points, and proposes a new non-integrable model close to the original for simulations.

Findings

The integrable line ends at a superwetting point with neutral interface energy.

A Bethe Ansatz confirms a dilogarithm identity for low-temperature expansion.

A new two-variable model exhibits phase and wetting transitions near zero temperature.

Abstract

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.