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Existence of phase transition of percolation on Sierpiński carpet lattices

Part of: Special processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  14 July 2016

Masato Shinoda
Masato Shinoda*
Affiliation:
Nara Women's University
*
∗ Postal address: Department of Mathematics, Faculty of Science, Nara Women's University, Kita-Uoya Nishimachi Nara 630 8506, Japan. Email address: shinoda@cc.nara-wu.ac.jp
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Abstract

We study Bernoulli bond percolation on Sierpiński carpet lattices, which is a class of graphs corresponding to generalized Sierpiński carpets. In this paper we give a sufficient condition for the existence of a phase transition on the lattices. The proof is suitable for graphs which have self-similarity. We also discuss the relation between the existence of a phase transition and the isoperimetric dimension.

Keywords

PercolationSierpiński carpetphase transitionisoperimetric dimension

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82B43: Percolation
Secondary: 82B26: Phase transitions (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 1 - 10
Copyright
Copyright © Applied Probability Trust 2002 

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