Reaction-diffusion processes and non perturbative renormalization group
Résumé
This article presents an approach, using non perturbative renormalization group methods, of critical phenomena in non equilibrium systems, with particular emphasis on reaction-diffusion processes. We first propose a review of the prevailing universality class among these systems, that of directed percolation, and present a detailed synthesis of the two main formalisms allowing to construct - from the Langevin equation or from the master equation respectively - a field theory for these processes. We then elaborate a generalization of the non perturbative renormalization group formalism (or effective average action method) to non equilibrium systems and derive very generic flow equations to describe reaction-diffusion processes. On the one hand, these flow equations enable us to bring out the first analytical determination of the (universal) critical exponents of directed percolation in all dimensions. On the other hand, we establish the full phase diagram of odd branching and annihilating random walks, which is quantitatively supported by numerical simulations. This analysis unveils non perturbative effects that qualitatively modify the commonly assumed (non universal) properties of this diagram - ensuing from perturbation theories.