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Graph homomorphisms and phase transitions

By Graham Brightwell and P. Winkler

Abstract

We model physical systems with “hard constraints” by the space Hom(G, H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H. For any assignment λ of positive real activities to the nodes of H, there is at least one Gibbs measure on Hom(G, H); when G is infinite, there may be more than one. When G is a regular tree, the simple, invariant Gibbs measures on Hom(G, H) correspond to node-weighted branching random walks on H. We show that such walks exist for every H and λ, and characterize those H which, by admitting more than one such construction, exhibit phase transition behavior

Topics: QA Mathematics
Publisher: Elsevier
Year: 1999
DOI identifier: 10.1006/jctb.1999.1899
OAI identifier: oai:eprints.lse.ac.uk:7474
Provided by: LSE Research Online
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