Exact results at the 2-D percolation point
Disordered Systems and Neural Networks
2009-10-30 v1 High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n_c in the infinite system limit; the bn correct bulk cumulants. b and b_n are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.
Cite
@article{arxiv.cond-mat/9709285,
title = {Exact results at the 2-D percolation point},
author = {P. Kleban and R. M. Ziff},
journal= {arXiv preprint arXiv:cond-mat/9709285},
year = {2009}
}
Comments
12 pages, 2 figures, LaTeX, submitted to Physical Review Letters