Anchored Critical Percolation Clusters and 2-D Electrostatics
Disordered Systems and Neural Networks
2009-11-11 v3 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.cond-mat/0605120,
title = {Anchored Critical Percolation Clusters and 2-D Electrostatics},
author = {P. Kleban and J. J. H. Simmons and R. M. Ziff},
journal= {arXiv preprint arXiv:cond-mat/0605120},
year = {2009}
}
Comments
4 pages, 1 (color) figure. More numerics, minor corrections, references added