Cardy, J.Täuber, Uwe C.2016-09-302016-09-301996-12-020031-9007http://hdl.handle.net/10919/73081A systematic theory for the diffusion–limited reaction processes A + A → ⊘ and A → (m + 1)A is developed. Fluctuations are taken into account via the field–theoretic dynamical renormalization group. For m even the mean field rate equation, which predicts only an active phase, remains qualitatively correct near d_c = 2 dimensions; but below d′_c ≈ 4/3 a nontrivial transition to an inactive phase governed by power law behavior appears. For m odd there is a dynamic phase transition for any d ≤ 2 which is described by the directed percolation universality class.4780 - 4783 page(s)application/pdfenIn CopyrightArticle - Refereedhttps://doi.org/10.1103/PhysRevLett.77.47807723