Field-theoretic analysis of directed percolation: Three-loop approximation

TL;DR

This paper employs a field-theoretic and renormalization group approach to analyze directed percolation, calculating critical exponents up to three-loop order to better understand its phase transition behavior.

Contribution

It provides a third-order perturbative calculation of critical exponents for directed percolation using advanced field-theoretic and renormalization techniques.

Findings

Critical exponents calculated to third order in perturbation theory.

Ultraviolet divergences determined through combined analytical and numerical methods.

Enhanced understanding of the universality class of directed percolation.

Abstract

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter $\varepsilon$, where $\varepsilon=4-d$ is a deviation from the upper critical dimension $d_c=4$. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.