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Abstract <p> 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon=4-d\)</EquationSource> </InlineEquation>. 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. </p>

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

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • M. Hnatič,
  • M. Kecer,
  • T. Lučivjanský,
  • L. Mižišin

摘要

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.