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Superscaling of percolation on rectangular domains
Hiroshi Watanabe1, Satoshi Yukawa, Nobuyasu Ito
1Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Furouchou, Chikusa-ku, Nagoya 464-8601, Japan.
Physical Review Letters
|December 17, 2004
Summary
We propose a new scaling function for percolation on rectangular domains. Monte Carlo simulations confirm this function, revealing a new exponent
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Percolation theory studies the connectivity of random networks.
- Understanding critical phenomena in finite-size systems is crucial.
Purpose of the Study:
- To propose a generalized scaling function for percolation on rectangular domains.
- To introduce and determine a new critical exponent 'a'.
Main Methods:
- Monte Carlo simulations were employed on square lattices.
- Bond percolation was simulated to analyze cluster existence probability.
Main Results:
- A scaling function F(epsilonL(y(t))R(a)) was proposed for percolation.
- The new exponent 'a' was found to be 0.14(1) for R>2.
- The proposed scaling function was well-satisfied by simulation data.
Conclusions:
- The study provides a robust scaling description for percolation on anisotropic domains.
- Superscaling is proposed for other critical quantities, extending the findings.