Resource title

Hard constraints and the Bethe Lattice: adventures at the interface of combinatorics and statistical physics

Resource image

image for OpenScout resource :: Hard constraints and the Bethe Lattice: adventures at the interface of combinatorics and statistical physics

Resource 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.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

Resource resource URL

http://eprints.lse.ac.uk/10602/

Resource license