The order parameter of the chiral Potts model

TL;DR

This paper verifies a longstanding conjecture about the order parameter of the chiral Potts model by employing an analyticity assumption and the broken rapidity line method, providing a significant theoretical confirmation.

Contribution

It demonstrates that under an analyticity assumption, the conjectured order parameter can be rigorously verified using the broken rapidity line approach.

Findings

Verification of the conjecture under the analyticity assumption

Application of the broken rapidity line method to the problem

Theoretical confirmation of the order parameter expression

Abstract

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is aware there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ``broken rapidity line'' approach pioneered by Jimbo, Miwa and Nakayashiki.