## 摘要

We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice Λ by ℓ bonds connecting the same adjacent vertices, thereby yielding the lattice Λ _{ℓ}. This relation is used to calculate the bond percolation threshold on Λ _{ℓ}. We show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality d≥2 but changes it on a one-dimensional lattice and quasi-one-dimensional infinite-length strips. We also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the N→∞ limits of several families of N-vertex graphs. Finally, we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as N→∞.

原文 | English |
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頁（從 - 到） | 676-700 |

頁數 | 25 |

期刊 | Journal of Statistical Physics |

卷 | 149 |

發行號 | 4 |

DOIs | |

出版狀態 | Published - 2012 十一月 1 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics