Persistence in the Voter model: continuum reaction-diffusion approach

Details Persistence in the Voter model: continuum reaction-diffusion approach Persistence in the Voter model: continuum reaction-diffusion approach

1997-11-15

arxiv.org/abs/cond-mat/9711148v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 3 figures, Latex, submitted to J. Phys. A (letters)

Scientific paper

10.1088/0305-4470/31/11/001

We investigate the persistence probability in the Voter model for dimensions d\geq 2. This is achieved by mapping the Voter model onto a continuum reaction-diffusion system. Using path integral methods, we compute the persistence probability r(q,t), where q is the number of ``opinions'' in the original Voter model. We find r(q,t)\sim exp[-f_2(q)(ln t)^2] in d=2; r(q,t)\sim exp[-f_d(q)t^{(d-2)/2}] for 24. The results of our analysis are checked by Monte Carlo simulations.

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