Anchored Critical Percolation Clusters and 2-D Electrostatics

Details Anchored Critical Percolation Clusters and 2-D Electrostatics Anchored Critical Percolation Clusters and 2-D Electrostatics

2006-05-04

arxiv.org/abs/cond-mat/0605120v3

Phys.Rev.Lett. 97 (2006) 115702

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevLett.97.115702

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.

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