Federico Benitez, Nicolas Wschebor
We present some exact results for Branching and Annihilating Random Walks. We compute the non-universal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the Directed Percolation universality class, and we show that the accepted scenario for the appearance of a phase transition in the Parity Conserving universality class is invalid. In order to obtain these results we perform an expansion in the branching rate around Pure Annihilation, a theory without branching. This expansion is possible because we manage to solve Pure Annihilation exactly in any dimension.
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http://arxiv.org/abs/1203.0235
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