Percolation phenomena in low and high density systems

L. Chayes, J. L. Lebowitz, V. Marinov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the 2D quenched-disordered q-state Potts ferromagnets and show that in the translation invariant measure, averaged over the disorder, at self-dual points any amalgamation of q-1 species will fail to percolate despite an overall (high) density of 1-q -1. Further, in the dilute bond version of these systems, if the system is just above threshold, then throughout the low temperature phase there is percolation of a single species despite a correspondingly small density. Finally, we demonstrate both phenomena in a single model by considering a "perturbation" of the dilute model that has a self-dual point. We also demonstrate that these phenomena occur, by a similar mechanism, in a simple coloring model invented by O. Häggström.

Original languageEnglish (US)
Pages (from-to)567-585
Number of pages19
JournalJournal of Statistical Physics
Volume129
Issue number3
DOIs
StatePublished - Nov 2007

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Critical phenomena
  • Percolation
  • Potts model

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