Hyperelliptic parametrisation of the generalised order parameter of the N=3 chiral Potts model

Abstract

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