Key points are not available for this paper at this time.
A systematic theory for the diffusion-limited reaction processes A+A0 and A (m+1) A is developed. Fluctuations are taken into account via the field-theoretic dynamical renormalization group. For even m, the mean field rate equation, which predicts only an active phase, remains qualitatively correct near d₂0ex{0ex}=0ex{0ex}2 dimensions; but below d₂^'4/3 a nontrivial transition to an inactive phase governed by power law behavior appears. For odd m, there is a dynamic phase transition for any d2 which is described by the directed percolation universality class.
Cardy et al. (1996) studied this question.