Vortex dynamics in a three-state model under cyclic dominance

Details Vortex dynamics in a three-state model under cyclic dominance Vortex dynamics in a three-state model under cyclic dominance

1999-07-22

arxiv.org/abs/cond-mat/9907333v1

Phys. Rev. E, 60 (1999) 3776

Physics

Condensed Matter

Statistical Mechanics

5 pages, 6 figures, to appear in PRE

Scientific paper

10.1103/PhysRevE.60.3776

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate which is increased by the spiral formation due to the cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle antiparticle system with density dependent pair creation rate. Numerical estimates for the critical indices of the vortex density ($\beta=0.29(4)$) and of its fluctuation ($\gamma=0.34(6)$) improve an earlier Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic voter model in two dimensions.

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