Following an introduction to nonequilibrium universality classes,
which occur in basic reaction-diffusion particle models I discuss
some results obtained by cluster mean-field approximations and
simulations of such models. These findings are unexpected by perturbative renormalization group (RG) methods, but are in agreement with non-perturbative RG. This suggests that diffusion may become relevant in case of competing reactions and nontrivial phase structures can emerge even in very simple system.
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