Critical branching-annihilating random walk of two species

The effect of blocking between different species occurring in low dimensions is investigated here numerically in case of particles following branching and annihilating random walk. It is shown that in two dimension simulations confirm the field theoretical results with logarithmic corrections. In one dimension however if particles exhibit hard core interaction there are two different universality classes depending on the spatial symmetry of the offspring production characterized with $\beta_S=0.5$ and $\beta_A=2$. Elaborated analysis of simulation data shows that the order parameter exponent $\beta$ does not depend on initial conditions or on diffusion rates of species but strong correction to scaling is observed. The particle density decay at the critical point follows $t^{-1/4}$ law with logarithmic corrections.