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Title: Gibbs states on random configurations

Gibbs states of a spin system with the single-spin space S=R{sup m} and unbounded pair interactions are studied. The spins are attached to the points of a realization γ of a random point process in R{sup n}. Under certain conditions on the model parameters we prove that, for almost all γ, the set G(S{sup γ}) of all Gibbs states is nonempty and its elements have support properties, explicitly described in the paper. We also show the existence of measurable selections γ→ν{sub γ}ϵG(S{sup γ}) (random Gibbs measures) and derive the corresponding averaged moment estimates.
Authors:
 [1] ; ;  [2] ;  [3]
  1. Department of Mathematics, University of York, York YO1 5DD (United Kingdom)
  2. Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld (Germany)
  3. Instytut Matematyki, Uniwersytet Marii Curie-Sklodowskiej, 20-031 Lublin (Poland)
Publication Date:
OSTI Identifier:
22306100
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; MATHEMATICAL MODELS; PAIRING INTERACTIONS; RANDOMNESS; SPIN