Renormalization group analysis of directed percolation process: Towards multiloop calculation of scaling functions
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910019855843328 |
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| author | Hnatič, Michal Kecer, Matej Lučivjanský, Tomáš Mižišin, Lukáš |
| author_facet | Hnatič, Michal Kecer, Matej Lučivjanský, Tomáš Mižišin, Lukáš |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalization group analysis of directed percolation process: Towards multiloop calculation of scaling functions Hnatič, Michal Kecer, Matej Lučivjanský, Tomáš Mižišin, Lukáš Statistical Mechanics 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. |
| title | Renormalization group analysis of directed percolation process: Towards multiloop calculation of scaling functions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.11369 |