arXiv:cond-mat/9709285·v1·cond-mat.dis-nn
Exact results at the 2-D percolation point
P. Kleban (1) · R. M. Ziff (2) ((1) Laboratory for Surface Science and Technology & Department of Physics and Astronomy, University of Maine, Orono, ME, (2) Department of Chemical Engineering, University of Michigan, Ann Arbor, MI)
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.
Comments: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letters