%0 Journal Article
%T Geometric structure of percolation clusters
%A Xiao Xu
%A Junfeng Wang
%A Zongzheng Zhou
%A Timothy M. Garoni
%A Youjin Deng
%J Physics
%D 2013
%I arXiv
%R 10.1103/PhysRevE.89.012120
%X We investigate the geometric properties of percolation clusters, by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo simulations, we study the probability that a given edge is not a bridge but has both its loop arcs in the same loop, and find that it is governed by the two-arm exponent. We then classify bridges into two types: branches and junctions. A bridge is a {\em branch} iff at least one of the two clusters produced by its deletion is a tree. Starting from a percolation configuration and deleting the branches results in a {\em leaf-free} configuration, while deleting all bridges produces a bridge-free configuration. Although branches account for $\approx 43%$ of all occupied bonds, we find that the fractal dimensions of the cluster size and hull length of leaf-free configurations are consistent with those for standard percolation configurations. By contrast, we find that the fractal dimensions of the cluster size and hull length of bridge-free configurations are respectively given by the backbone and external perimeter dimensions. We estimate the backbone fractal dimension to be $1.643\,36(10)$.
%U http://arxiv.org/abs/1309.7244v3