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Graph homomorphisms and phase transitions

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

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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
Official URL: http://www.elsevier.com
Additional Information: © 1999 Academic Press
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 17 Feb 2010 12:51
URL: http://eprints.lse.ac.uk/7474/

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