Theory of Branching and Annihilating Random Walks

Details Theory of Branching and Annihilating Random Walks Theory of Branching and Annihilating Random Walks

1996-09-17

arxiv.org/abs/cond-mat/9609151v2

Phys. Rev. Lett. {\bf 77} (1996) 4780

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevLett.77.4780

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 $d_c' \approx 4/3$ a nontrivial transition to an inactive phase governed by power law behavior appears. For $m$ odd there is a dynamic phase transition for any $d \leq 2$ which is described by the directed percolation universality class.

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