Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring

Abstract

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. {\bf 68}, 3060 (1992)], studied branching annihilating random walks (BAW) 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: $β/\nuh = {1/2}$, $\nuv/\nuh = {7/4}$, $\gamma =0$, $\delta =2/7$, $\eta =0$, $z=8/7$, and ${\delta }_h=9/2$.

18 pages (+16 Fig.), LaTeX

References in corpus (1)

• Generalized Scaling for Models with Multiple Absorbing States

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