Gibbs states on random configurations

Journal Article · Fri Aug 01 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4891992· OSTI ID:22306100

Daletskii, Alexei ^[1]; Kondratiev, Yuri; Pasurek, Tanja ^[2]; Kozitsky, Yuri ^[3]

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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)

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

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONFIGURATION
MATHEMATICAL MODELS
PAIRING INTERACTIONS
RANDOMNESS
SPIN