Exactly Solvable Models

Chiral Potts Model is used to study the commensurate-incommensurate phase transitions.

This simulation is used for the Chiral Clock Model.

This model was found to lie on a high genus curve.
More details are in the following talk
Integrable Chiral Potts Model: Its history and relation with Mathematics where the Boltzmann weights of the Chiral Potts model are given in product form. They satisfied the Star-Triangle relations and are therefore integrable. Its relation to six-vertex models and the representation of the Quantum groups are also briefly described. The transfer matrices also satisfy certain relations, which are called functional relations. These relations are very important which can be used to obtain the specific heat of the Chiral Potts model.

The superintegrable model is a special case of the chiral Potts, with Ising-like spectrums. The following talks elaborate on the model:
Eigenvectors for the Superintegrable Chiral Potts model

Eigenvectors for the Superintegrable Chiral Potts Model II

Spontaneous Magnetization in the Integrable Chiral Potts Model: Two Different Approaches

Spontaneous Magnetization in the Integrable Chiral Potts Model: Cracking the Determinant