Critical behavior for mixed site-bond directed percolation

Abstract

We study mixed site-bond directed percolation on 2D and 3D lattices by using time-dependent simulations. Our results are compared with rigorous bounds recently obtained by Liggett and by Katori and Tsukahara. The critical fractions $p_{site}^c$ and $p_{bond}^c$ of sites and bonds are extremely well approximated by a relationship reported earlier for isotropic percolation, $(\log p_{site}^c/\log p_{site}^{c^*}+\log p_{bond}^c/\log p_{bond}^{c^*} = 1)$, where $p_{site}^{c^*}$ and $p_{bond}^{c^*}$ are the critical fractions in pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]