Exact results at the 2-D percolation point

Details Exact results at the 2-D percolation point Exact results at the 2-D percolation point

1997-09-25

arxiv.org/abs/cond-mat/9709285v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 2 figures, LaTeX, submitted to Physical Review Letters

Scientific paper

10.1103/PhysRevB.57.R8075

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.

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