Hard constraints and the bethe lattice: adventures at the interface of combinatorics and statistical physics
| dc.creator | Brightwell, Graham R. | |
| dc.creator | Winkler, Peter | |
| dc.date | 2003-04-28 | |
| dc.date.accessioned | 2026-07-07T04:57:33Z | |
| dc.date.available | 2026-07-07T04:57:33Z | |
| dc.description | Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for the study of phase transition. In this paper we survey recent work (concentrating on joint work of the authors) in which hard-constraint systems are modeled by the space $\hom(G,H)$ of homomorphisms from an infinite graph $G$ to a fixed finite constraint graph $H$. These spaces become sufficiently tractable when $G$ is a regular tree (often called a Cayley tree or Bethe lattice) to permit characterization of the constraint graphs $H$ which admit multiple invariant Gibbs measures. Applications to a physics problem (multiple critical points for symmetry-breaking) and a combinatorics problem (random coloring), as well as some new combinatorial notions, will be presented. | |
| dc.identifier | https://arxiv.org/abs/math/0304468 | |
| dc.identifier | http://arxiv.org/abs/math/0304468 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 3, 605--624 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67300 | |
| dc.subject | Combinatorics | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B20, 68R10 | |
| dc.title | Hard constraints and the bethe lattice: adventures at the interface of combinatorics and statistical physics | |
| dc.type | text |