Explicit isoperimetric constants and phase transitions in the random-cluster model
| dc.creator | Haggstrom, Olle | |
| dc.creator | Jonasson, Johan | |
| dc.creator | Lyons, Russell | |
| dc.date | 2000-08-24 | |
| dc.date | 2001-04-17 | |
| dc.date.accessioned | 2026-07-07T04:36:58Z | |
| dc.date.available | 2026-07-07T04:36:58Z | |
| dc.description | The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster parameter $q\geq 1$. Among these, the main ones are the absence of percolation for the free random-cluster measure at the critical value, and examples of planar regular graphs with regular dual where $\pc^\f (q) > \pu^\w (q)$ for $q$ large enough. The latter follows from considerations of isoperimetric constants, and we give the first nontrivial explicit calculations of such constants. Such considerations are also used to prove non-robust phase transition for the Potts model on nonamenable regular graphs. | |
| dc.identifier | https://arxiv.org/abs/math/0008191 | |
| dc.identifier | http://arxiv.org/abs/math/0008191 | |
| dc.identifier | Ann. Probab. 30 (2002), 443--473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59795 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B20 | |
| dc.title | Explicit isoperimetric constants and phase transitions in the random-cluster model | |
| dc.type | text |