A remark on Dobrushin's uniqueness theorem (Q1140371)
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scientific article; zbMATH DE number 3678913
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on Dobrushin's uniqueness theorem |
scientific article; zbMATH DE number 3678913 |
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A remark on Dobrushin's uniqueness theorem (English)
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1979
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It is shown that for a lattice system with compact one-point state space and translation invariant interaction, whose ``formal Hamiltonian'' is given by \(H(s) = \sum_X \Phi_X(s)\), \(X\) running through all finite subsets of \(\mathbb Z^d\), the hypothesis of Dobrushin's theorem on the uniqueness of Gibbs measures -- see \textit{R. L. Dobrushin} [Teor. Veroyatn. Primen. 13, 201--229 (1968; Zbl 0177.45202)] is satisfied if \[ \sum_{c\in X} \Vert \Phi_X \Vert\cdot (\vert X\vert - 1) < 1.\]
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Dobrushin's uniqueness theorem
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lattice system
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translation invariant interaction
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