Abstract
We consider the branching and annihilating random walk \(A\to 2A\) and \(2A\to 0\) with reaction rates σ and λ, respectively, and hopping rate D, and study the phase diagram in the λ/D,σ/D) plane. According to standard mean-field theory, this system is in an active state for all σ/D≥0, and perturbative renormalization suggests that this mean-field result is valid for d>2; however, nonperturbative renormalization predicts that for all d there is a phase transition line to an absorbing state in the λ/D,σ/D) plane. We show here that a simple single-site approximationreproduces with minimal effort the nonperturbative phase diagram both qualitatively and quantitatively for all dimensions d>2. We expect the approach to be useful for other reaction-diffusion processes involving absorbing state transitions.
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Canet, L., Hilhorst, H.J. Single-Site Approximation for Reaction-Diffusion Processes. J Stat Phys 125, 517–531 (2006). https://doi.org/10.1007/s10955-006-9206-8
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DOI: https://doi.org/10.1007/s10955-006-9206-8