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AB percolation on bond-decorated graphs

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  14 July 2016

Martin J. B. Appel  and
John C. Wierman
Martin J. B. Appel*
Affiliation:
University of Iowa
John C. Wierman*
Affiliation:
The Johns Hopkins University
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA.
∗∗ Postal address: Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Abstract

It is known [8] that a certain class of bond-decorated graphs exhibits multiple AB percolation phase transitions. Sufficient conditions are given under which the corresponding AB percolation critical probabilities may be identified as points of intersection of the graph of a certain polynomial with the boundary of the percolative region of an associated two-parameter bond-site percolation model on the underlying undecorated graph. The main result of the article is used to prove that the graphs in [8] exhibit multiple AB percolation critical probabilities. The possibility of identifying AB percolation critical exponents with corresponding limits for the bond-site model is discussed.

Keywords

PERCOLATIONBOND-SITE MODELCRITICAL PROBABILITIESCRITICAL EXPONENTS

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B43: Percolation
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 153 - 166
Copyright
Copyright © Applied Probability Trust 1993 

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References

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