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

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.