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Percolation Phenomena in Low and High Density Systems | | L. Chayes
; J.L.Lebowitz
; V. Marinov
; | | Date: |
19 Jan 2007 | | Subject: | Statistical Mechanics | | Abstract: | We consider the 2d quenched--disordered $q$--state Potts ferromagnets and show that at self--dual points the amalgamation of the first $q-1$ 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. H"aggstr"om.} | | Source: | arXiv, cond-mat/0701468 | | Services: | Forum | Review | PDF | Favorites | |
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