Brightwell, Graham and Winkler, P.
(1999)
*Graph homomorphisms and phase transitions.*
Journal of Combinatorial Theory, Series B, 77 (2).
pp. 221-262.
ISSN 0095-8956

## 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.

Item Type: | Article |
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Official URL: | http://www.elsevier.com |

Additional Information: | © 1999 Academic Press |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 17 Feb 2010 12:51 |

Last Modified: | 20 Feb 2021 03:25 |

URI: | http://eprints.lse.ac.uk/id/eprint/7474 |

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