arXiv subjects

Matej Kecer

Publications and source records attributed to Matej Kecer.

4 recordsLinked to original sources

arXiv2026

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

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.

cond-mat.stat-mech↗

arXiv2025

Field-theoretic Analysis of Dynamic Isotropic Percolation: Three-loop Approximation

The general epidemic process is a paradigmatic model in non-equilibrium statistical physics displaying a continuous phase transition between active and absorbing states.The dynamic isotropic percolation universality class captures its universal properties, which we aim to quantitatively study by means of the field-theoretic formulation of the model augmented with a perturbative renormalization group analysis. The main purpose of this work consists in determining the critical dynamic exponent $z$ to the three-loop approximation. This allows us to finalize the quantitative description of the dynamic isotropic percolation class to this order of perturbation theory. The calculations are performed within the dimensional regularization with the minimal subtraction scheme and actual perturbative expansions are carried out in a formally small parameter $\epsilon$, where $\epsilon = 6 - d$ is a deviation from the upper critical dimension $d_c = 6$.

cond-mat.stat-mech↗

arXiv2023

Anomalous Kinetics of a Multi-Species Reaction-Diffusion System: Effect of Random Velocity Fluctuations

Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of kinetic rate equations is not sufficient and the effect of density fluctuations has to be properly taken into account. Our aim here is to analyze a particular multi-species reaction-diffusion system characterized by reactions $\textit{A} +\textit{A} \rightarrow (\emptyset, A),$ $\textit{A} +\textit{B} \rightarrow \textit{A}$ at and below its critical dimension $d_c = 2$. In particular, we investigate effect of thermal fluctuations on the reaction kinetics, which are generated by means of random velocity field modelled by a stochastic Navier-Stokes equations. Main theoretical tool employed is field-theoretic perturbative renormalization group. The analysis is performed to the first order of the perturbation scheme (one-loop approximation).

cond-mat.stat-mech↗

arXiv2023

Two-species reaction-diffusion system in the presence of random velocity fluctuations

We study random velocity effects on a two-species reaction-diffusion system consisting of three reaction processes $A + A \rightarrow (\varnothing, A),A+B \rightarrow A$. Using the field-theoretic perturbative renormalization group we analyze this system in the vicinity of its upper critical dimension $d_c = 2$. Velocity ensemble is generated by means of stochastic Navier-Stokes equations. In particular, we investigate the effect of thermal fluctuations on reaction kinetics. The overall analysis is performed to the one-loop approximation and possible macroscopic regimes are identified.

cond-mat.stat-mech↗