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Title: Gibbs states on random configurations

Abstract

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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; MATHEMATICAL MODELS; PAIRING INTERACTIONS; RANDOMNESS; SPIN

Citation Formats

Daletskii, Alexei, Kondratiev, Yuri, Pasurek, Tanja, and Kozitsky, Yuri. Gibbs states on random configurations. United States: N. p., 2014. Web. doi:10.1063/1.4891992.
Daletskii, Alexei, Kondratiev, Yuri, Pasurek, Tanja, & Kozitsky, Yuri. Gibbs states on random configurations. United States. doi:10.1063/1.4891992.
Daletskii, Alexei, Kondratiev, Yuri, Pasurek, Tanja, and Kozitsky, Yuri. Fri . "Gibbs states on random configurations". United States. doi:10.1063/1.4891992.
@article{osti_22306100,
title = {Gibbs states on random configurations},
author = {Daletskii, Alexei and Kondratiev, Yuri and Pasurek, Tanja and Kozitsky, Yuri},
abstractNote = {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.},
doi = {10.1063/1.4891992},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 55,
place = {United States},
year = {Fri Aug 01 00:00:00 EDT 2014},
month = {Fri Aug 01 00:00:00 EDT 2014}
}