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

TL;DR

This paper provides a detailed three-loop field-theoretic analysis of dynamic isotropic percolation, refining the critical dynamic exponent calculation within the renormalization group framework for non-equilibrium phase transitions.

Contribution

It advances the understanding of dynamic isotropic percolation by computing the critical dynamic exponent to three-loop order using perturbative renormalization group methods.

Findings

Critical dynamic exponent $z$ calculated to three-loop order.

Enhanced quantitative description of the dynamic isotropic percolation class.

Application of dimensional regularization and minimal subtraction scheme.

Abstract

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 $d_c = 6$.