Solution of voter model dynamics on annealed small-world networks

Details Solution of voter model dynamics on annealed small-world networks Solution of voter model dynamics on annealed small-world networks

2003-08-19

arxiv.org/abs/cond-mat/0308366v2

Phys. Rev. E 69, 016109 (2004)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 4 figures, published version. Added section with extension to generic number of nearest neighbors

Scientific paper

10.1103/PhysRevE.69.016109

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $\tau$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $\tau$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.

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