Gibbs states on random configurations
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, University of York, York YO1 5DD (United Kingdom)
- Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld (Germany)
- Instytut Matematyki, Uniwersytet Marii Curie-Sklodowskiej, 20-031 Lublin (Poland)
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.
- OSTI ID:
- 22306100
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
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