Three-state Potts model on a triangular lattice.

We study the phase diagram of the three-state Potts model on a triangular lattice with general interactions (ferro/antiferromagnetic) between nearest neighbor spins. When the interactions along two lattice-vector directions are antiferromagnetic and infinitely strong, this model becomes equivalent to a six-vertex model and exhibits a first-order (KDP) transition from an ordered phase into a critical phase. Comparing the excitations occurred by relaxing the restriction of infinite-strength interactions and those in the eight-vertex model, we analytically obtain the critical index for those excitations and demonstrate the existence of a critical phase for the case of finite antiferromagnetic interactions in two directions and ferromagnetic interactions in the other direction. When the interactions are antiferro-magnetic in all three directions, Monte Carlo simulations show that a first-order line emerges from the KDP point and separates completely an ordered phase and a disordered phase. Along the special line where all three antiferromagnetic interactions have the same strength, the cell-spin analysis reveals that the symmetry of the ground states is dual to the symmetry of the n = 3 ferromagnetic cubic model which is known to exhibit a first-order phase transition.