The challenge of the chiral Potts model

TL;DR

This paper discusses the longstanding challenges in solving the chiral Potts model, highlighting the difficulty of deriving the order parameter despite its known solvability via the Yang-Baxter relation.

Contribution

It presents the derivation of the conjectured order parameter for the chiral Potts model, completed in 2005, which was previously unresolved.

Findings

Derivation of the chiral Potts model's order parameter in 2005

Confirmation of the model's solvability via Yang-Baxter relation

Discussion of the challenges in solving the model

Abstract

The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. Here we discuss that derivation.