Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree (Q360219)
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scientific article; zbMATH DE number 6201535
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree |
scientific article; zbMATH DE number 6201535 |
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Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree (English)
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26 August 2013
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One considers Hamiltonian models with a nearest neighbor interaction and uncountably many spin values on a Cayley tree, and more especially, one refers to the problem of describing infinite-volume Gibbs measures corresponding to a given Hamiltonian. Various properties are derived for the Hammerstein's operator of order \(k\), and one gives a sufficient condition on the Hamiltonian for the model to have a unique translation-invariant splitting Gibbs measure.
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Cayley tree
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configuration
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Gibbs measures
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uniqueness
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