  We study a three-state Potts model extended by allowing cyclic dominance
between the states as it appears for the rock-scissors-paper game. Monte Carlo
simulations are performed on a square lattice when 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 that yields a self-organizing pattern even at low
temperatures. The differences and similarities are discussed between the
present model and the half-filled, driven lattice gases with repulsive
interaction.
