Renormalization group analysis of directed percolation process: Towards multiloop calculation of scaling functions

TL;DR

This paper advances the theoretical understanding of directed percolation by extending the renormalization group analysis to three-loop order, developing new calculation techniques, and verifying previous results.

Contribution

It introduces a semi-analytic method for three-loop calculations in directed percolation, enabling more precise scaling function analysis.

Findings

Mapped many three-loop diagrams onto existing results

Developed techniques for calculating novel three-loop diagrams

Verified two-loop results with the new method

Abstract

In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop order in the expansion parameter $\varepsilon = 4-d$. We show that a large group of the necessary three-loop Feynman diagrams can be mapped onto already existing three-loop results, and develop a technique for the calculation of the remaining -- truly novel -- ones. The described semi-analytic procedure is further used to verify existing two-loop results. The main aim of this study is to provide an update on this ongoing work, as full three-loop calculations utilizing the described procedure are in progress.