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

TL;DR

This paper investigates how cyclic dominance in a three-state Potts model influences phase transitions, revealing that such dominance prevents ordering and promotes self-organizing patterns, contrasting with traditional models.

Contribution

It introduces a novel extension of the three-state Potts model incorporating cyclic dominance, demonstrating its impact on phase transition behavior through Monte Carlo simulations.

Findings

Cyclic dominance destroys the critical phase transition.

Self-organizing patterns emerge at low temperatures.

Differences from driven lattice gases are discussed.

Abstract

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.