Critical Behavior of Percolation Process Influenced by Random Velocity Field: One-Loop Approximation

TL;DR

This paper uses renormalization group techniques to analyze how a random velocity field affects the critical behavior of directed percolation near phase transition, considering finite correlation times.

Contribution

It introduces a three-parameter expansion approach to study the influence of advecting velocity fields on percolation criticality using field-theoretic methods.

Findings

Identification of stable fixed points under perturbations.

Analysis of the impact of velocity field correlations on phase transition.

Extension of the model to include finite correlation times.

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.