Nonlinear Phenomena in Complex Systems, 2025, Vol.28, No.4, pp.377

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2025, Vol.28, No.4, pp.377 - 388

Critical Exponents of Dynamic Percolation Universality Class: the Renormalization Group Approach

Michal Hnatič, Matejč Kecer, Tomáš Lučivjanský, Mikhail V. Kompaniets, Lukáš Mižišin, and Yurii G. Molotkov

In this study we focus on the non-equilibrium phase transition whose asymptotic critical behavior is governed by the dynamic isotropic percolation universality class. In order to quantitatively characterize universal properties associated with this class, we employ a field-theoretic formulation of the model augmented with perturbative renormalization group technique. Utilizing such approach enables us to systematically compute the critical exponents in higher orders of perturbation theory. In particular, we perform an analysis to the three-loop precision. To this order we determine the renormalization constants and present relations for critical exponents in terms of critical dimensions. Finally, we also present numerically estimated values of critical exponents obtained from perturbation theory.

Key words: non-equilibrium phase transitions, dynamic isotropic percolation process, perturbative field-theoretic renormalization group, multi-loop calculations

DOI: https://doi.org/10.5281/zenodo.17950360

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