## Abstract

We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts p and that of the ordinary bonds p. The system has a critical phase in which the percolating probability P takes an intermediate value 0<P<1. Using generating function approach, we calculate the fractal exponent ψ of the root clusters to show that ψ varies continuously with p in the critical phase. We confirm numerically that the distribution n_{s} of cluster size s in the critical phase obeys a power law n_{s} s^{-}τ, where τ satisfies the scaling relation τ=1+ ψ^{-}1. In addition the critical exponent β (p) of the order parameter varies as p, from β 0.164694 at p=0 to infinity at p= p_{c} =5/32.

Original language | English |
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Article number | 046101 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 82 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2010 Oct 1 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics