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

Iwan Jensen
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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: $β/\nuh = {1/2}$, $\nuv/\nuh = {7/4}$, $γ= 0$, $δ= {2/7}$, $η= 0$, $z = {8/7}$, and $δ_{h} = {9/2}$.

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Iwan Jensen. 1994-05-04. Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring. https://doi.org/10.1103/physreve.50.3623

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