Profile and scaling of the fractal exponent of percolations in complex networks

Details Profile and scaling of the fractal exponent of percolations in complex networks Profile and scaling of the fractal exponent of percolations in complex networks

2010-09-29

arxiv.org/abs/1009.6009v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 10 figures

Scientific paper

We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that the cooperative systems in growing network models often undergo an infinite order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, the transition point is very hard for numerical simulations to find because the system is in a critical state outside the ordered phase. We propose a finite size scaling form for the order parameter by using the fractal exponent, which enables us to determine the transition points and critical exponents numerically for infinite order transitions as well as standard second order transitions. We confirm the validity of our scaling hypothesis through the Monte-Carlo simulations for bond percolations in two network models; the growing random network model, which exhibits an infinite order transition, and its reconstructed network, which shows a conventional second order transition.

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