Incipient spanning cluster on small-world networks
Department of Theoretical Physics, Umeå University -
901 87 Umeå, Sweden
Corresponding author: email@example.com
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