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Abstract: We study the critical behavior of the pair annihilation model PAM withdiffusion in one, two and three dimensions, using the pair approximation PAand Monte Carlo simulation. Of principal interest is the dependence of thecritical creation rate, lambda c, on the diffusion probability D, inparticular, whether survival is possible at arbitrarily small creation rates,for sufficiently rapid diffusion. Whilst the PA predicts that in any spatialdimension d \geq 1, lambda c -> 0 at some diffusion probability D* < 1, Katoriand Konno Physica A {\bf 186}, 578 1992 showed rigorously that for d \leq2, one has lambda c > 0 for any D<1. Our simulation results are consistent withthis theorem. In two dimensions, the extinction region becomes narrow as Dapproaches unity, following lambda c \propto \exp- m{const.}-1-D^\gamma,with gamma = 1.412. In three dimensions we find D* = 0.3333. The simulationresults confirm that the PAM belongs to the directed percolation universalityclass.



Author: Adriana Gomes Dickman, Ronald Dickman

Source: https://arxiv.org/







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