title: Branching-rate expansion around annihilating random walks.
abstract: We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.
authors.affiliation: LPTMC, CNRS-UMR 7600, Université Pierre et Marie Curie, 75252 Paris, France.
authors.forename: Federico
authors.initials: F
authors.lastname: Benitez
authors.forename: Nicolás
authors.initials: N
authors.lastname: Wschebor
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical