title: Role of diffusion in branching and annihilation random walk models.
abstract: Different branching and annihilating random walk models are investigated by the cluster mean-field method and simulations in one and two dimensions. In the case of the A-->2A , 2A--> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by the nonperturbative renormalization group method [Phys. Rev. Lett. 92, 255703 (2004)]]. The same type of survey for the A-->2A , 4A--> 0 model results in a reentrant phase diagram, similar to that of the 2A-->3A , 4A--> 0 model [Phys. Rev. E 69, 036112 (2004)]]. Simulations of the A-->2A , 4A--> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.
authors.affiliation: Research Institute for Technical Physics and Materials Science, P. O. Box 49, H-1525 Budapest, Hungary.
authors.forename: Géza
authors.initials: G
authors.lastname: Odor