Transport properties of directed percolation clusters at the upper critical dimension

TL;DR

This paper investigates the transport properties of directed percolation clusters at the upper critical dimension, calculating logarithmic corrections to mean-field scaling for various observables using field theory and renormalization group techniques.

Contribution

It provides the first detailed calculation of logarithmic corrections for multiple transport observables in directed percolation at the upper critical dimension.

Findings

Logarithmic corrections to connectivity probability derived

Next-to-leading order corrections for two-point resistance computed

Multifractal moments of current distribution analyzed with corrections

Abstract

We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field theory and renormalization group methods we calculate these logarithmic corrections up to and including the next to leading correction for a variety of observables, viz. the connectivity, i.e., the probability that two given points are connected, the average two-point resistance and some of the fractal masses describing percolation clusters. Furthermore, we study logarithmic corrections for the multifractal moments of the current distribution on directed percolation clusters.