Numerical calculation of scaling exponents of percolation process in the framework of renormalization group approach

TL;DR

This paper employs the renormalization group theory to numerically calculate the scaling exponents of directed bond percolation near its critical point, focusing on the epsilon-expansion around the upper critical dimension.

Contribution

It introduces a numerical method for calculating renormalization group functions in directed percolation using Feynman diagrams without explicitly computing renormalization constants.

Findings

Calculated anomalous dimensions using Feynman diagrams

Applied epsilon-expansion near critical dimension d_c=4

Utilized null momentum subtraction scheme for computations

Abstract

We use the renormalization group theory to study the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the $\epsilon$-expansion where $\epsilon$ is a deviation from the upper critical dimension $d_c = 4$. Within this procedure anomalous dimensions $\gamma$ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the $R$ operation, and for computational purposes we choose the null momentum subtraction scheme.