Some Exact Results on Bond Percolation

Shu Chiuan Chang, Robert Shrock

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

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. This relation is used to calculate the bond percolation threshold on Λ. 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
頁(從 - 到)676-700
頁數25
期刊Journal of Statistical Physics
149
發行號4
DOIs
出版狀態Published - 2012 11月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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