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We study a three-state Potts model extended by allowing cyclic dominancebetween the states as it appears for the rock-scissors-paper game. Monte Carlosimulations are performed on a square lattice when varying the temperature andthe strength of cyclic dominance. It is shown that the critical phasetransition from the disordered state to the ordered one is destroyed by thecyclic dominance that yields a self-organizing pattern even at lowtemperatures. The differences and similarities are discussed between thepresent model and the half-filled, driven lattice gases with repulsiveinteraction.Comment: 4 pages, 4 figure

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