Chiral Potts model

The chiral Potts model is a spin model on a planar lattice in statistical mechanics studied by Helen Au-Yang Perk and Jacques Perk, among others. It may be viewed as a generalization of the Potts model, and as with the Potts model, the model is defined by configurations which are assignments of spins to each vertex of a graph, where each spin can take one of ${\displaystyle N}$ values. To each edge joining vertices with assigned spins ${\displaystyle n}$ and ${\displaystyle n'}$, a Boltzmann weight ${\displaystyle W(n,n')}$ is assigned. For this model, chiral means that ${\displaystyle W(n,n')\neq W(n',n)}$. When the weights satisfy the Yang–Baxter equation, it is integrable, in the sense that certain quantities can be exactly evaluated.

For the integrable chiral Potts model, the weights are defined by a high genus curve, the chiral Potts curve.^[1][2] Unlike the other solvable models,^[3][4] whose weights are parametrized by curves of genus less or equal to one, so that they can be expressed in terms of trigonometric functions, rational functions for the genus zero case, or by theta functions for the genus 1 case, this model involves high genus theta functions, for which the theory is less well-developed.

The related chiral clock model, which was introduced in the 1980s by David Huse and Stellan Ostlund independently, is not exactly solvable, in contrast to the chiral Potts model.