Vortex dynamics in a three-state model under cyclic dominance

TL;DR

This paper investigates vortex dynamics in a three-state cyclic voter model, revealing how vortex-antivortex pairs form, move, and annihilate, with numerical estimates of critical indices improving previous studies.

Contribution

It provides new numerical estimates of critical indices for vortex density and fluctuations, enhancing understanding of vortex behavior in cyclic dominance models.

Findings

Vortices and antivortices perform random walks and annihilate.

Spiral formation increases vortex-antivortex pair creation.

Critical indices for vortex density and fluctuations are estimated.

Abstract

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.