2007/01/31 by L. Chayes, Joel L. Lebowitz, J. L. Lebowitz +2 · 1 citation
Mathematics · Physics and Astronomy · #Condensed matter physics #Critical point (mathematics) #Electrical resistivity and conductivity #Ferromagnetism #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation theory #Percolation threshold #Perturbation (astronomy) #Phase transition #Physics #Potts model #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-007-9408-8
26 pages, v2: some more details in the Appendix, fixed typographical errors and included references to physics literature (following referees suggestions)
arxiv created 2007/05/18 · openalex publication_date 2007/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.