Anchored Critical Percolation Clusters and 2-D Electrostatics

TL;DR

This paper explores the relationship between critical percolation cluster densities anchored to edges in 2D systems and electrostatic potentials, revealing a superposition principle and broadening the known connection between percolation and electrostatics.

Contribution

It introduces a novel link between 2D percolation cluster densities and electrostatic dipole potentials, extending previous findings and suggesting a more general applicability.

Findings

Cluster densities relate to electrostatic dipole potentials.

A superposition and factorization principle applies.

Evidence suggests broader validity of the electrostatics-percolation connection.

Abstract

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2-D electrostatic dipoles, and that a kind of superposition {\it cum} factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.