Branching annihilating random walks with parity conservation on a square lattice

Using Monte Carlo simulations we have studied the transition from an "activ e" steady state to an absorbing "inactive'' state for two versions of the b ranching annihilating random walks with parity conservation on a square lat tice. in the first model the randomly walking particles annihilate when the y meet and the branching process creates two additional particles; in the s econd case we distinguish particles and antiparticles created and annihilat ed in pairs. Quite distinct critical behavior is found in the mio cases, ra ising the question of what determines universality in these kinds of system s. [S1063-651X(99)51503-1].