Critical exponents for branching annihilating random walks with an even number of offspring

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks (BAWs) with n=1–5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd n the models belong to the universality class of directed percolation. For even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation. In this article I study the BAW with n=4 using time-dependent simulations and finite-size scaling, obtaining precise estimates for various critical exponents. The results are consistent with the conjecture: β/${\nu }_{\mathrm{\perp }}$=1/2, ${\nu }_{\mathrm{\parallel }}$/${\nu }_{\mathrm{\perp }}$=7/4, γ=0, δ=2/7, η=0, and ${\mathrm{\delta }}_{\mathit{h}}$=9/2. These critical exponents characterize, respectively, the dependence of the order parameter (β/${\nu }_{\mathrm{\perp }}$) and relaxation time (${\nu }_{\mathrm{\parallel }}$/${\nu }_{\mathrm{\perp }}$) on system size, the growth of fluctuations (γ) close to the critical point, the long-time behavior of the probability of survival (δ) and average number of particles (η) when starting at time zero with just two particles, and finally the decay of the order parameter (${\mathrm{\delta }}_{\mathit{h}}$) at the critical point in the presence of an external source.