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Exact Results for Average Cluster Numbers in Bond Percolation on Lattice
Strips
Exact Results for Average Cluster Numbers in Bond Percolation on Lattice
Strips
2004-07-02
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arxiv.org/abs/cond-mat/0407070v2
Phys. Rev. E70 (2004) 056130
Physics
Condensed Matter
Statistical Mechanics
16 pages, revtex, 7 eps figures
Scientific paper
10.1103/PhysRevE.70.056130
We present exact calculations of the average number of connected clusters per site, $$, as a function of bond occupation probability $p$, for the bond percolation problem on infinite-length strips of finite width $L_y$, of the square, triangular, honeycomb, and kagom\'e lattices $\Lambda$ with various boundary conditions. These are used to study the approach of $$, for a given $p$ and $\Lambda$, to its value on the two-dimensional lattice as the strip width increases. We investigate the singularities of $$ in the complex $p$ plane and their influence on the radii of convergence of the Taylor series expansions of $$ about $p=0$ and $p=1$.
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