Some Exact Results on Bond Percolation

Shu Chiuan Chang, Robert Shrock

研究成果: Article同行評審

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 十一月 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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