  Using Monte Carlo simulations we have studied the transition from an "active"
steady state to an absorbing "inactive" state for two versions of the branching
annihilating random walks with parity conservation on a square lattice. In the
first model the randomly walking particles annihilate when they meet and the
branching process creates two additional particles; in the second case we
distinguish particles and antiparticles created and annihilated in pairs. Quite
distinct critical behavior is found in the two cases, raising the question of
what determines universality in this kind of systems.

Statistical Mechanics