Directed-bond percolation subjected to synthetic compressible velocity fluctuations: Renormalization group approach

We study the directed-bond percolation process (sometimes called the Gribov process because it formally resembles Reggeon field theory) in the presence of irrotational velocity fluctuations with long-range correlations. We use the renormalization group method to investigate the phase transition between an active and an absorbing state. All calculations are in the one-loop approximation. We calculate stable fixed points of the renormalization group and their regions of stability in the form of expansions in three parameters $(\varepsilon,y,\eta)$. We consider different regimes corresponding to the Kraichnan rapid-change model and a frozen velocity field.