Conservation laws and universality in branching annihilating random walks

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Abstract
Takayasu and Tretyakov (1992) studied branching annihilating random walks with n=1-5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd n the models belong to the universality class of directed percolation. For even n the particle number is conserved modulo two and the critical behaviour is not compatible with directed percolation. Branching annihilating random walks with n=4 additional process (spontaneous annihilation) which breaks the conservation law are studied. The inclusion of spontaneous annihilation, even at very small rates, leads to directed percolation critical behaviour.

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