Critical Phase of Bond Percolations on Growing Networks

Details Critical Phase of Bond Percolations on Growing Networks Critical Phase of Bond Percolations on Growing Networks

2010-04-06

arxiv.org/abs/1004.0795v1

Phys. Rev. E 81, 051105 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 figures; accepted for publication in Physical Review E

Scientific paper

10.1103/PhysRevE.81.051105

The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s \propto s^{-\tau}$ in the whole range of open bond probability $p$. The exponent $\tau$ and the fractal exponent $\psi$ are also derived as a function of $p$ and the degree exponent $\gamma$, and are found to satisfy the scaling relation $\tau=1+\psi^{-1}$. Numerical results with several network sizes are quite well fitted by a finite size scaling for a wide range of $p$ and $\gamma$, which gives a clear evidence for the existence of a critical phase.

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