# 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:

- 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)

- 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}

}

DOI: 10.1063/1.4891992

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