Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold

TL;DR

This paper investigates the multifractal characteristics of current distribution in 3D random resistor networks at the percolation threshold, providing detailed moment measurements and critical exponent estimates.

Contribution

It offers new measurements of higher moments of current distribution and estimates of critical exponents at the percolation threshold for 3D resistor networks.

Findings

Measured second, fourth, and sixth moments of current distribution.

Estimated the ratio t/nu as 2.282(5).

Analyzed multifractal properties at the percolation threshold.

Abstract

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth moments of the current distribution, finding {\it e.g.\/} that $t/\nu=2.282(5)$ where $t$ is the conductivity exponent and $\nu$ is the correlation length exponent.