Role of diffusion in branching and annihilation random walk models

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→0̸ model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by the nonperturbative renormalization group method [ L. Canet et al. Phys. Rev. Lett. 92 255703 (2004)]. The same type of survey for the A→2A, 4A→0̸ model results in a reentrant phase diagram, similar to that of the 2A→3A, 4A→0̸ model [ G. Ódor Phys. Rev. E 69 036112 (2004)]. Simulations of the A→2A, 4A→0̸ 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.