Mapping functions and critical behavior of percolation on rectangular domains

Details Mapping functions and critical behavior of percolation on rectangular domains Mapping functions and critical behavior of percolation on rectangular domains

2008-09-22

arxiv.org/abs/0809.3636v1

Physics

Condensed Matter

Statistical Mechanics

17 pages with 6 figures

Scientific paper

10.1103/PhysRevE.78.041131

The existence probability $E_p$ and the percolation probability $P$ of the bond percolation on rectangular domains with different aspect ratios $R$ are studied via the mapping functions between systems with different aspect ratios. The superscaling behavior of $E_p$ and $P$ for such systems with exponents $a$ and $b$, respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev. Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order approximation of the mapping functions $f_R$ and $g_R$ for $E_p$ and $P$, respectively; the exponents $a$ and $b$ can be obtained from numerically determined mapping functions $f_R$ and $g_R$, respectively.

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