Abstract
We introduce a branching annihilating random walker process with two species, particles A and B, which diffuse creating particles of opposite kind (A→A+B, B→B+A) and annihilating instantaneously (A+B→0) when they meet. The model is defined in a one dimensional discrete lattice. For particles A and B, the rate of jumping are pA and pB, and the rate of branching (1−pA) and (1−pB), respectively (0≤pA, pB≤1). In the [pA, pB]-plane it is found two different phases: the vacuum state and the active phase with finite density of particles. The system undergoes irreversible second order phase transitions between these states along a critical line. Monte Carlo results show that the transitions belong to the same universality class as directed percolation.
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