A three-state cyclic voter model extended with Potts energy

Abstract

The cyclically dominated voter model on a square lattice is extended by taking into consideration the variation of Potts energy during the nearest neighbor invasions. We have investigated the effect of surface tension on the self- organizing patterns maintained by cyclic invasions. A geometrical analysis is also developed tp study the three-color patterns. These investigations indicate clearly that in the "voter model" limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening. Conversely, in the presence surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance.