Persistence in the Voter model: continuum reaction-diffusion approach

We investigate the persistence probability in the Voter model for dimensions d greater than or equal to 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, r), where q is the number of 'opinions' in the original Voter model. We find r(q, t) similar to exp[-f(2)(q)(lnt)(2)] in d = 2; r(q, r) similar to exp[-(f)d(q)t((d-2)/2)] for 2 < d < 4; r(q, t) similar to exp[-f(4)(q)t/ln t] in d = 4; and r(q, I) similar to exp[-f(d)(q)t] for d > 4. The results of our analysis are checked by Monte Carlo simulations.