Free energy of the three-state $\tau_2(t_q)$ model as a product of elliptic functions

TL;DR

This paper expresses the free energy of the three-state $ au_2(t_q)$ model using elliptic functions, marking a novel application of hyperelliptic parametrization to the chiral Potts model for N > 2.

Contribution

It introduces a new elliptic function representation of the free energy for the three-state $ au_2(t_q)$ model using hyperelliptic parametrization, a first for N > 2.

Findings

Free energy expressed as products of Jacobi elliptic functions.

First application of hyperelliptic parametrization to N > 2 chiral Potts model.

Provides a new analytical approach to the model's free energy.

Abstract

{We show that the free energy of the three-state $\tau_2(t_q)$ model can be expressed as products of Jacobi elliptic functions, the arguments being those of an hyperelliptic parametrization of the associated chiral Potts model. This is the first application of such a parametrization to the $N$-state chiral Potts free energy problem for $N > 2$.