# Passive advection of percolation process: Two-loop approximation

## TL;DR

This paper investigates the directed percolation process under external velocity fields using a field-theoretic approach, analyzing fixed points with a two-loop approximation to understand phase transition behavior.

## Contribution

It introduces a two-loop renormalization group analysis of directed percolation in a velocity field, extending previous one-loop studies and incorporating Kraichnan ensemble effects.

## Key findings

- Fixed point structure characterized at two-loop level
- Velocity fluctuations influence percolation spreading
- Enhanced understanding of phase transition dynamics

## Abstract

The paradigmatic model of the directed percolation process is studied near its second order phase transition between an absorbing and an active state. The model is first expressed in a form of Langevin equation and later rewritten into a field-theoretic formulation. The ensuing response functional is then analyzed employing Feynman diagrammatic technique and perturbative renormalization group method. Percolation process is assumed to occur in external velocity field, which has an additional effect on spreading properties. Kraichnan rapid change ensemble is used for generation of velocity fluctuations. The structure of the fixed points structure is obtained within the two-loop approximation.