Spatial Dependence of Microscopic Percolation Conduction

TL;DR

This paper investigates how microscopic percolation conduction in two-dimensional networks relates to conformal transformations, confirming theoretical predictions at the percolation threshold for square lattices.

Contribution

It verifies the conformal invariance of electrical conductance in 2D percolation networks at the critical threshold, providing empirical support for theoretical models.

Findings

Conformal invariance holds at the percolation threshold for square lattices.

Electrical conductance relates via conformal transformation in 2D percolation networks.

Verification supports theoretical predictions of conductance behavior at criticality.

Abstract

In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary should be related by a conformal transformation to the conductance from one point to another in an unbounded network. We verify that this works at the percolation threshold for the square.