Gribov process advected by the synthetic compressible velocity ensemble: Renormalization Group Approach

TL;DR

This paper investigates how irrotational, long-range correlated velocity fluctuations influence the phase transition in the Gribov process using a one-loop renormalization group analysis, revealing different regimes and stability conditions.

Contribution

It applies the perturbative renormalization group to the Gribov process with compressible velocity fields, exploring effects of finite correlation time on phase transition behavior.

Findings

Identification of stable fixed points and their stability regions.

Analysis of rapid-change and frozen velocity regimes.

Insights into the influence of velocity correlations on phase transition.

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 ab- sorbing 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 $(\epsilon,y,\eta)$- expansion. Different regimes corresponding to the rapid- change limit and frozen velocity field are discussed.