Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time

TL;DR

This paper investigates how velocity fluctuations with finite correlation time and compressibility influence the phase transition in directed percolation, using renormalization group analysis to identify stable regimes.

Contribution

It introduces a one-loop renormalization group analysis of directed percolation with Gaussian velocity fluctuations, accounting for compressibility and finite correlation time.

Findings

Identification of stable fixed points in different velocity regimes

Analysis of the impact of compressibility on phase transition behavior

Numerical determination of fixed point structures

Abstract

The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by the Gaussian self-similar ensemble with finite correlation time. We employ the renormalization group in order to analyze a combined effect of the compressibility and finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The renormalization procedure is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are calculated in the one-loop approximation within the three-parameter $(\eps,y,\eta)$-expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed, and their fixed points' structure is determined in numerical fashion.