caa a22 4500 467893004 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10955-006-9206-8 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9206-8 Single-Site Approximation for Reaction-Diffusion Processes [Elektronische Daten] [L. Canet, H. Hilhorst] 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. Springer Science+Business Media, LLC, 2006 reaction-diffusion problems nationallicence branching processes nationallicence Canet L. Service de Physique de l‘;État Condensé, Orme des Merisiers - CEA Saclay, 91191, Gif-sur-Yvette Cedex, France aut Hilhorst H. Laboratoire de Physique Théorique, Bâtiment 210, Université de Paris-Sud 91405, Orsay Cedex, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/3(2006-11-01), 517-531 0022-4715 125:3<517 2006 125 10955 https://doi.org/10.1007/s10955-006-9206-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9206-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Canet L. Service de Physique de l‘;État Condensé, Orme des Merisiers - CEA Saclay, 91191, Gif-sur-Yvette Cedex, France aut NATIONALLICENCE 700 1- Hilhorst H. Laboratoire de Physique Théorique, Bâtiment 210, Université de Paris-Sud 91405, Orsay Cedex, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/3(2006-11-01), 517-531 0022-4715 125:3<517 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer