Three-state Potts model in combination with the rock-scissors-paper game.

We study a three-state Potts model extended by allowing cyclic dominance between the states as exemplified in the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice while varying the temperature and the strength of cyclic dominance. It is shown that the critical phase transition from the disordered state to the ordered one is destroyed by the cyclic dominance, which yields a self-organizing pattern even at low temperatures. The differences and similarities are discussed between the present model and half-filled, driven lattice gases with repulsive interaction.