title: Branching and annihilating random walks: exact results at low branching rate.
abstract: We present some exact results on the behavior of branching and annihilating random walks, both in the directed percolation and parity conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the branching rate around the nontrivial pure annihilation (PA) model, whose correlation and response function we compute exactly. With this, the nonuniversal threshold value for having a phase transition in the simplest system belonging to the directed percolation universality class is found to coincide with previous nonperturbative renormalization group (RG) approximate results. We also show that the parity conserving universality class has an unexpected RG fixed point structure, with a PA fixed point which is unstable in all dimensions of physical interest.
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: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted