Volume 104, Number 1, October 2013
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||15 November 2013|
Profile and scaling of the fractal exponent of percolations in complex networks
1 Graduate School of Information Sciences, Tohoku University - 6-3-09, Aramaki-Aza-Aoba, Sendai, 980-8579, Japan
2 Faculty of Medicine, Toho University - 5-21-16, Omori- nishi, Ota-ku, Tokyo 143-8540, Japan
3 Department of Physics, Graduate School of Science, Hokkaido University - Kita 10-jo Nisi 8-tyome, Sapporo, Japan
Received: 17 August 2013
Accepted: 14 October 2013
We propose a novel finite-size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite-order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite-size scaling technique does not work. In our finite-size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite-order transition as well as a standard second-order transition. We confirm the validity of our scaling hypothesis through Monte Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite-order transition occurs, and the configuration model, where a second-order transition occurs.
PACS: 64.60.ah – Percolation / 64.60.aq – Networks / 89.75.Hc – Networks and genealogical trees
© EPLA, 2013
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