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Different branching and annihilating random walk models are investigated bycluster mean-field method and simulations in one and two dimensions. In case ofthe A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusiondependence in the phase diagram as was found recently by non-perturbativerenormalization group method (L. Canet et al., cond-mat/0403423). The same typeof survey for the A -> 2A, 4A -> 0 model results in a reentrant phase diagram,similar to that of 2A -> 3A, 4A -> 0 model (G. \'Odor, PRE {\bf 69}, 036112(2004)). Simulations of the A -> 2A, 4A -> 0 model in one and two dimensionsconfirm the presence of both the directed percolation transitions at finitebranching rates and the mean-field transition at zero branching rate. In twodimensions the directed percolation transition disappears for strong diffusionrates. These results disagree with the predictions of the perturbativerenormalization group method.Comment: 4 pages, 4 figures, 1 table include

Role of diffusion in branching and annihilation random walk models