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Percolation Phenomena in Low and High Density Systems

L. Chayes·J. L. Lebowitz·V. Marinov
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Abstract

We consider the 2D quenched--disordered $q$--state Potts ferromagnets and show that 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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L. Chayes, J. L. Lebowitz, V. Marinov. 2007-05-18. Percolation Phenomena in Low and High Density Systems. https://doi.org/10.1007/s10955-007-9408-8

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