Free energy of the three-state τ 2 ( t q ) model as a product of elliptic functions

Abstract

We show that the free energy of the three-state 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.