Percolation Phenomena in Low and High Density Systems
Abstract
We consider the 2D quenched--disordered --state Potts ferromagnets and show that at self--dual points any amalgamation of species will fail to percolate despite an overall (high) density of . 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. H\"aggstr\"om.
Keywords
Cite
@article{arxiv.cond-mat/0701468,
title = {Percolation Phenomena in Low and High Density Systems},
author = {L. Chayes and J. L. Lebowitz and V. Marinov},
journal= {arXiv preprint arXiv:cond-mat/0701468},
year = {2009}
}
Comments
26 pages, v2: some more details in the Appendix, fixed typographical errors and included references to physics literature (following referees suggestions)