Positive fixed points of quadratic operators and Gibbs measures

We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. Recently, solving this integral equation some periodic (in particular translation-invariant) splitting Gibbs measures were found. In this paper we give three constructions of new sets of non-translation-invariant splitting Gibbs measures. Our constructions are based on known solutions of the integral equation.Mathematics Subject Classifications (2010). 82B05, 82B20 (primary); 60K35 (secondary)

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Positive fixed points of quadratic operators and Gibbs measures

Cited by 12 publications

References 20 publications

New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree

New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree

Fixed points of Lyapunov integral operators and Gibbs measures

Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree

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