Two-Species Branching Annihilating Random Walks with One Offspring

The last decades have seen considerable efforts to understand nonequilibrium absorbing phase transitions from an active phase into an absorbing phase consisting of absorbing states [1]. Once the system is trapped into an absorbing state, it can never escape from the state. Various one dimensional lattice models exhibiting absorbing transitions have been studied, and most of them turn out to belong to one of two universality classes, the directed percolation (DP) and the directed Ising (DI) universality classes. While models with the Ising symmetry between absorbing states belong to the DI class, models in the DP class have no symmetry between absorbing states [1,2]. It is generally accepted that the dimensionality and the symmetry between absorbing states play important roles in determining the universality classes as in equilibrium critical phenomena. To find out new universality classes, it is natural to study models with higher symmetries than the Ising symmetry. To achieve a higher symmetry, such as the Potts symmetry, one may increase the number of absorbing states. However, the models with higher symmetries investigated so far turn out to be always active and are only critical at the annihilation fixed point of zero branching rate [3]. A recent field theoretical study may provide a possible explanation for this [4]. Although there is no stable absorbing phase, critical behaviors near the annihilation fixed point are non-trivial and form new universality classes [4,5]. In systems with more than two equivalent absorbing states, there are various kinds of domain walls (or kinks) that cannot cross over each other to retain the order