Fluctuations near nonequilibrium phase transitions to nonuniform states

Abstract

The influence of local fluctuations on a symmetry-breaking chemical instability is considered in terms of concepts developed in the theory of equilibrium phase transitions. It is shown that for infinite systems some predictions of the mean-field theory are qualitatively incorrect. Indeed, the fluctuations destroy any structure in one- and two-dimensional systems and some of them in three dimensions. The stabilizing effect of the finite dimensions on these structures is also discussed, and it is shown that in this case the fluctuations induce a weak first-order transition near the critical point of the mean-field theory.