PHASE-DIAGRAM OF A 6-STATE CHIRAL POTTS-MODEL

We study the phase diagram of an isotropic six-state chiral Potts mode l on a square lattice by means of both exact and numerical methods. Th e phase diagram of this model presents many similarities with the phas e diagrams of the Ashkin-Teller model or the models studied by Zamolod chikov and Monarstirskii. A remarkable line globally invariant under a transformation generalizing the Kramers-Wannier duality seems to corr espond to a first order transition line up to a bifurcation point wher e this line splits into two second order lines. All the numerical calc ulations are compared with exact results which can be performed using a canonical elliptic parametrization of this model. The bifurcation po int is found to correspond to the intersection of a generalized self-d ual line with an algebraic curve. This curve corresponds to the set of points of the phase diagram for which a non-trivial infinite symmetry group of the model degenerates into a finite group of order six. The agreement between numerical and analytical results is very good.