## Abstract

Using finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdös-Rényi network at p=0.5 and the random network under the Achlioptas process at p=1. Using both the fixed point of the size ratio s _{2}/s _{1} and the straight line of lns _{1}, where s _{1} and s _{2} are the reduced sizes of the largest and the second-largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5≤p≤1. From the slopes of lns _{1} and ln ^{(}s _{2} ^{/}s _{1} ^{)} ^{′} at the critical point, we get critical exponents β and ν of the phase transitions. At 0.5≤p≤0.8, it is found that β, ν, and s _{2}/s _{1} at critical point are unchanged and the phase transitions belong to the same universality class. When p≥0.9, β, ν, and s _{2}/s _{1} at critical point vary with p and the universality class of phase transitions depends on p.

Original language | English |
---|---|

Article number | 061110 |

Journal | Physical Review E |

Volume | 85 |

Issue number | 6 |

DOIs | |

State | Published - 8 Jun 2012 |

Externally published | Yes |

## ASJC Scopus subject areas

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