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

Abstract

The direct bond percolation process (Gribov process) is studied in the presence of irrotational velocity fluctuations with long-range correlations. The perturbative renormalization group is employed in order to analyze the effects of finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The calculation is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are obtained within the three-parameter (ε, y, η)-expansion. Different regimes corresponding to the rapidchange limit and frozen velocity field are discussed.

Active-to-absorbing phase transition subjected to the velocity fluctuations in the frozen limit case

“…Following the works [7,8] we consider a generalization of the original Kraichnan model where the advection-diffusion problem of non-interacting admixture has been studied. As some progress in this direction has already been made [9,10,11,12,13,14], our main aim here is to elucidate in detail the case of frozen velocity limit [8,15]. The main theoretical tool is the field-theoretic approach [16] with subsequent Feynman diagrammatic technique and renormalization group (RG) approach, which allows us to determine the large-scale behavior, which is of special interest from macroscopic point of view.…”