Precise determination of the conductivity exponent of 3d percolation using "Percola"

TL;DR

This paper reports a highly precise determination of the conductivity exponent in 3D percolation using extensive computational resources and advanced extrapolation techniques.

Contribution

The study introduces a novel high-precision computational approach with correction-to-scaling analysis for determining the conductivity exponent in 3D percolation.

Findings

Conductivity exponent t/ν = 2.26 ± 0.04

Correction exponent ω ≈ 1.4

Used 20 months of CPU time on 'Percola'

Abstract

Using 20 months of CPU time on our special purpose computer ``Percola'' we determined the exponent for the normal conductivity at the threshold of three-dimensional site and bond percolation. The extrapolation analysis taking into account the first correction to scaling gives a value of $t/\nu = 2.26\pm 0.04$ and a correction exponent $\omega$ around 1.4.