Critical Behaviour Of Directed Percolation In The Presence Of Synthetic Velocity Field

TL;DR

This paper investigates how a synthetic velocity field affects the critical behavior of directed percolation using renormalization group techniques, identifying universality classes and stability regions.

Contribution

It introduces a field-theoretic approach to analyze directed percolation under advective velocity fields with finite correlation time, extending understanding of universality classes.

Findings

Identification of fixed points and their stability regions.

Analysis near critical dimension using three-parameter expansion.

Determination of influence of velocity field on critical exponents.

Abstract

Using perturbative renormalization group we study the influence of random velocity field on the critical behaviour of directed bond percolation process near its second-order phase transition between absorbing and active phase. We consider Kraichnan model with finite correlation time for modelling advecting velocity field. Using functional integral representation we are able to apply field-theoretic renormalization group to determine possible universality classes. The model is analyzed near its critical dimension by means of three-parameter expansion in $\epsilon,\delta,\eta$, where $\epsilon$ is the deviation from the Kolmogorov scaling, $\delta$ 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 evaluated to the leading order in the perturbation scheme.