Mapping functions and critical behavior of percolation on rectangular domains.
The existence probability E_{p} and the percolation probability P of 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 [Phys. Rev. Lett. 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.
Watanabe
Hiroshi
H
Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Furouchou, Chikusa-ku, Nagoya 464-8601, Japan. hwatanabe@is.nagoya-u.ac.jp
Hu
Chin-Kun
CK