Hyperelliptic parametrization of the generalized order parameter of the N=3 chiral Potts model

TL;DR

This paper demonstrates that for the N=3 chiral Potts model, the order parameter function can be expressed using hyperelliptic functions, providing a new parametrization approach for partition and correlation functions.

Contribution

The paper introduces a hyperelliptic parametrization of the order parameter function for N=3, advancing the understanding of the model's mathematical structure.

Findings

The order parameter function S(t_p) can be expressed using hyperelliptic functions.

The hyperelliptic parametrization simplifies the analysis of the N=3 chiral Potts model.

This approach links the model's weights to hyperelliptic functions, enabling new calculations.

Abstract

It has been known for some time that the Boltzmann weights of the chiral Potts model can be parametrized in terms of hyperelliptic functions, but as yet no such parametrization has been applied to the partition and correlation functions. Here we show that for N=3 the function $S(t_p)$ that occurs in the recent calculation of the order parameters can be expressed quite simply in terms of such a parametrization.