Two-species branching annihilating random walks with one offspring

Abstract

We study the effects of hard core (HC) interactions between different species of particles on two-species branching annihilating random walks with one offspring(BAW$_2$(1)). The single-species model belongs to the directed percolation (DP) universality class. In the BAW$_2$(1) model, a particle creates one particle of the same species in its neighborhood with the probability $σ(1-p)$ and of the different species with $(1-σ)(1-p)$, where $p$ is the hopping probability. Without HC interactions, this model always exhibits the DP-type absorbing transition for all $σ$. Even with HC interactions, the nature of the phase transitions does not change except near $σ=0$, where the HC interaction destabilizes and completely wipes away the absorbing phase. The model is always active except at the annihilation fixed point of zero branching rate ($p=1$). Critical behavior near the annihilation fixed point is characterized by exponents $β= ν_\perp =1/2$ and $ν_{||} = 1$.