Some Exact Results on Bond Percolation

Shu Chiuan Chang, Robert Shrock

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1 Citation (Scopus)


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→∞.

Original languageEnglish
Pages (from-to)676-700
Number of pages25
JournalJournal of Statistical Physics
Issue number4
Publication statusPublished - 2012 Nov

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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