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 ${\beta }_S=0.5$ and ${\beta }_A=2$. Elaborate 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. By systematic numerical simulations the critical point properties have been explored and initial condition dependence of the dynamical exponents $Z$ and $\alpha$ 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.

6 pages, 10 figures included, final form

References in corpus (4)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Does hardcore interaction change absorbing type critical phenomena?
• Nonequilibrium Kinetic Ising Models: Phase Transition and Universality Classes in One Dimension
• Critical behaviour of annihilating random walk of two species with exclusion in one dimension

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• Hard core particle exclusion effects in low dimensional non-equilibrium phase transitions
• An Operational Definition of Topological Order
• The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion
• Dynamics-dependent criticality in models with q absorbing states
• Stability of vacuum in coupled directed percolation processes
• One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate