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arXiv · 0809.3636

Mapping functions and critical behavior of percolation on rectangular domains

Hiroshi Watanabe·Chin-Kun Hu
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Abstract

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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Hiroshi Watanabe, Chin-Kun Hu. 2008-09-22. Mapping functions and critical behavior of percolation on rectangular domains. https://doi.org/10.1103/physreve.78.041131

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