Three-state chiral Potts models on the triangular lattice: a Monte Carlo study

The q-state chiral Potts model can describe systems that exhibit rich phase diagrams (see, for instance, ref. [l]) and interesting physical properties like commensurate-incommensurate transitions [2]. The chiral Potts model has been extensively studied in the last few years from the point of view of exactly solvable models. Au-Yang et al. discovered integrable cases for the q-state chiral Potts model [3,4], which happens to be the first solvable model with genus greater than one parametrization (see, for instance, ref. [5]). These breakthroughs renewed the interest in these models. In a previous study [6] extensive Monte Carlo simulations have been performed for the three-state isotropic chiral Potts model on a square lattice. The relationship between exact solvability and criticality have been clarified in this model where these notions no longer coincide, in contrast with many models in statistical mechanics. The phase diagram of the chiral Potts model