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Abstract <p>The universal properties of the dynamic isotropic percolation process are analyzed employing the field-theoretic perturbative renormalization group approach. In particular, our aim is to discuss recent developments related to the three-loop calculations of the dynamic exponent <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_9173_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(z\)</EquationSource> <!--PhysPart2570068Hnatic-m1--> </InlineEquation>. The model is studied in the vicinity of the upper critical dimension <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_9173_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\({{d}_{{\text{c}}}} = 6\)</EquationSource> <!--PhysPart2570068Hnatic-m2--> </InlineEquation> by means of dimensional regularization and accompanied by the minimal subtraction method for an extraction of ultraviolet divergences. Preliminary results are presented for selected topologies of three-loop Feynman diagrams appearing in the Dyson equation for the propagator of the model.</p>

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Dynamic Isotropic Percolation Process: Three-Loop Approximation

  • 期刊论文

  • 发表日期：

    2025年10月25日

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  • M. Hnatič,
  • M. Kecer,
  • T. Lučivjanský,
  • L. Mižišin,
  • Yu. G. Molotkov

摘要

Abstract

The universal properties of the dynamic isotropic percolation process are analyzed employing the field-theoretic perturbative renormalization group approach. In particular, our aim is to discuss recent developments related to the three-loop calculations of the dynamic exponent \(z\) . The model is studied in the vicinity of the upper critical dimension \({{d}_{{\text{c}}}} = 6\) by means of dimensional regularization and accompanied by the minimal subtraction method for an extraction of ultraviolet divergences. Preliminary results are presented for selected topologies of three-loop Feynman diagrams appearing in the Dyson equation for the propagator of the model.