| Issue |
Europhys. Lett.
Volume 55, Number 6, September II 2001
|
|
|---|---|---|
| Page(s) | 762 - 766 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2001-00346-7 | |
| Published online | 01 December 2003 | |
Incipient spanning cluster on small-world networks
Department of Theoretical Physics, Umeå University -
901 87 Umeå, Sweden
Corresponding author: ozana@tp.umu.se
Received:
23
April
2001
Accepted:
4
July
2001
We analyze the scaling properties of the largest cluster size for the site
percolation problem on small-world graphs.
It is shown how the presence of the extra length-scale, the small-world
crossover length ξ, influences the fractal dimension D of the spanning cluster.
Using the results for dimension d=2 we find
the critical exponent τ governing the cluster size distribution
. This implies that τ is universal and independent of
d in agreement with the conjecture by Moore and Newman (
Phys. Rev. E, 62 (2000) 7059).
PACS: 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, 2001
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