CONSERVATION-LAWS AND UNIVERSALITY IN BRANCHING ANNIHILATING RANDOM-WALKS

Recently, Takayasu and Tretyakov 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. In this paper branching annihilating random walks with n = 4 plus an 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.