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Percolation Phenomena in Low and High Density Systems

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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.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, USA

    L. Chayes

  2. Department of Mathematics, Rutgers University, New Brunswick, NJ, USA

    J. L. Lebowitz

  3. Department of Physics, Rutgers University, New Brunswick, NJ, USA

    V. Marinov

Authors
  1. L. Chayes
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  2. J. L. Lebowitz
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  3. V. Marinov
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Correspondence to V. Marinov.

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Chayes, L., Lebowitz, J.L. & Marinov, V. Percolation Phenomena in Low and High Density Systems. J Stat Phys 129, 567–585 (2007). https://doi.org/10.1007/s10955-007-9408-8

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  • DOI: https://doi.org/10.1007/s10955-007-9408-8

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