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

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

1994-05-04

arxiv.org/abs/cond-mat/9405006v1

Physics

Condensed Matter

18 pages (+16 Fig.), LaTeX

Scientific paper

10.1103/PhysRevE.50.3623

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: $\beta/\nuh = {1/2}$, $\nuv/\nuh = {7/4}$, $\gamma = 0$, $\delta = {2/7}$, $\eta = 0$, $z = {8/7}$, and $\delta_{h} = {9/2}$.

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