Logarithmic corrections to scaling in critical percolation and random resistor networks

TL;DR

This paper investigates the critical behavior of percolation in six dimensions, focusing on logarithmic corrections to scaling for geometrical and transport properties using field theory and renormalization group methods.

Contribution

It provides a detailed analysis of fluctuation-induced logarithmic corrections to scaling, including calculations for correlation functions, cluster masses, and transport properties in high-dimensional percolation.

Findings

Derived logarithmic correction terms for correlation functions.

Calculated masses of backbone, red bonds, and shortest path.

Analyzed the average resistance and multifractal moments in resistor networks.

Abstract

We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up to and including the next to leading correction. Our study comprehends the percolation correlation function, i.e., the probability that 2 given points are connected, and some of the fractal masses describing percolation clusters. To be specific, we calculate the mass of the backbone, the red bonds and the shortest path. Moreover, we study key transport properties of percolation as represented by the random resistor network. We investigate the average 2-point resistance as well as the entire family of multifractal moments of the current distribution.