Theory of Branching and Annihilating Random Walks

Abstract

A systematic theory for the diffusion--limited reaction processes $A+A\to 0$ and $A\to (m+1)A$ 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 $d_c^{\prime }\approx 4/3$ a nontrivial transition to an inactive phase governed by power law behavior appears. For $m$ odd there is a dynamic phase transition for any $d\le 2$ which is described by the directed percolation universality class.

4 pages, revtex, no figures; final version with slight changes, now accepted for publication in Phys. Rev. Lett

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