Tunneling and Non-Universality in Continuum Percolation Systems

TL;DR

This paper investigates the critical conductivity exponent in tunneling-percolation systems, revealing that considering a three-dimensional model explains the discrepancy between experimental results and theoretical predictions.

Contribution

It introduces a three-dimensional model of tunneling-percolation that accounts for experimental observations, resolving previous discrepancies with one-dimensional theories.

Findings

Experimental exponents are within a limited range close to $t_0$.

Three-dimensional modeling aligns theory with experimental data.

Discrepancies are due to the limited proximity to the percolation threshold.

Abstract

The values obtained experimentally for the conductivity critical exponent in numerous percolation systems, in which the interparticle conduction is by tunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where $t_0$ is the universal conductivity exponent. These latter values are however considerably smaller than those predicted by the available ``one dimensional"-like theory of tunneling-percolation. In this letter we show that this long-standing discrepancy can be resolved by considering the more realistic "three dimensional" model and the limited proximity to the percolation threshold in all the many available experimental studies