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arXiv · cond-mat/9609151

Theory of Branching and Annihilating Random Walks

John Cardy·Uwe C. Täuber
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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 $d_c' \approx 4/3$ 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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John Cardy, Uwe C. Täuber. 1996-10-23. Theory of Branching and Annihilating Random Walks. https://doi.org/10.1103/physrevlett.77.4780

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