Passive advection in a percolation process: Two-loop approximation

We study an instructive model of the directed percolation process near its second-order phase transition between absorbing and active states. We first express the model as a Langevin equation and then rewrite it in a field theory formulation. Using the Feynman diagram technique and the perturbative renormalization group method, we then analyze the resulting response functional. The percolation process is assumed to occur in an external velocity field, which has an additional effect on the properties of spreading. We use the Kraichnan rapid-change ensemble to generate velocity fluctuations. We obtain the structure of the set of fixed points in the two-loop approximation.