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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Critical phenomena
- Potts model