Percolation Phenomena in Low and High Density Systems

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.

26 pages, v2: some more details in the Appendix, fixed typographical errors and included references to physics literature (following referees suggestions)

References in corpus (1)

• The onset of jamming as the sudden emergence of an infinite $k$-core cluster