Critical branching-annihilating random walk of two species

Abstract

The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional simulations confirm the field theoretical results with logarithmic corrections. In one dimension, however, if particles exhibit hard core interaction I confirm the very recent predictions of Kwon et al. [PRL {\bf 85}, 1682 (2000)] that there are two different universality classes depending on the spatial symmetry of the offspring production characterized by $β_S=0.5$ and $β_A=2$. Elaborate analysis of simulation data shows that the order parameter exponent $β$ does not depend on initial conditions or on diffusion rates of species but strong correction to scaling is observed. By systematic numerical simulations the critical point properties have been explored and initial condition dependence of the dynamical exponents $Z$ and $α$ is shown. In the case of a random initial state the particle-density decay at the critical point follows the $t^{-1/4}$ law with logarithmic corrections.