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

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 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 to calculate the remaining—truly novel—ones. The described semianalytic 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.