Superscaling of percolation on rectangular domains.
For percolation on (RL)xL two-dimensional rectangular domains with a width L and aspect ratio R, we propose that the existence probability of the percolating cluster E(p)(L,epsilon,R) as a function of L, R, and deviation from the critical point epsilon can be expressed as F(epsilonL(y(t))R(a)), where y(t) identical with1/nu is the thermal scaling power, a is a new exponent, and F is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with a=0.14(1) for R>2. We also propose superscaling for other critical quantities.
Watanabe
Hiroshi
H
Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Furouchou, Chikusa-ku, Nagoya 464-8601, Japan.
Yukawa
Satoshi
S
Ito
Nobuyasu
N
Hu
Chin-Kun
CK