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

Abstract

Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase. Antonov-Kraichnan model with finite correlation time is used for description of advecting velocity field. The field-theoretic renormalization group approach is applied for getting information about asymptotic large scale behavior of the model under consideration. The model is analyzed near its critical dimension through three-parameter expansion in {\epsilon}, {\delta}, {\eta}, where {\epsilon} is the deviation from the Kolmogorov scaling, {\delta} is the deviation from the critical space dimension {d_c} and {\eta} is the deviation from the parabolic dispersion law for the velocity correlator. Fixed points with corresponding regions of stability are determined to the leading order in the perturbation scheme.