Anchored Critical Percolation Clusters and 2-D Electrostatics

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.

4 pages, 1 (color) figure. More numerics, minor corrections, references added

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• A formula for crossing probabilities of critical systems inside polygons
• Factorization of correlations in two-dimensional percolation on the plane and torus
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Exact factorization of correlation functions in 2-D critical percolation
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• Factorization of percolation density correlation functions for clusters touching the sides of a rectangle
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• The density of critical percolation clusters touching the boundaries of strips and squares
• Cluster densities at 2-D critical points in rectangular geometries
• General solution of an exact correlation function factorization in conformal field theory
• First Column Boundary Operator Product Expansion Coefficients