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An alternative proof of some percolation threshold (p c ) using the idea of self-organized criticality |
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| Authors: | H. F. Chau K. S. Cheng |
| Affiliation: | (1) Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, 61801 Urbana, IL, USA;(2) Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong;(3) Present address: School of Natural Sciences, Institute for Advanced Study, Olden Lane, 08540 Princeton, NJ, USA |
| Abstract: | Summary By means of a well-developed method in self-organized criticality, we can obtain the lower bound for the percolation threshold (p c) of the corresponding site percolation problem. In some special cases, we have proved that such lower bounds are indeed the percolation thresholds. We can reproduce some well-known percolation thresholds of various lattices including the Cayley trees and Kock curves in this framework. |
| Keywords: | Renormalization-group fractal and percolation studies of phase transitions |
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