Critical behavior of percolation process influenced by a random velocity field: One–loop approximation

Using the perturbation renormalization group, we investigate the influence of a random velocity field on the critical behavior of the directed-bond percolation process near its second-order phase transition between the absorbing and active phases. We use the Antonov–Kraichnan model with a finite correlation time to describe the advecting velocity field. To obtain information about the large-scale asymptotic behavior of the model, we use the field theory renormalization group approach. We analyze the model near its critical dimension via a three-parameter expansion in $\epsilon$, $\delta$, and $\eta$, where $\epsilon$ is the deviation from the Kolmogorov scaling, $\delta$ is the deviation from the critical space dimension, and $\eta$ is the deviation from the parabolic dispersion law for the velocity correlator. We find the fixed points with the corresponding stability regions in the leading order in the perturbation scheme.