Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

We consider models with nearest-neighbor interactions and with the set \([0,1]\) of spin values, on a Cayley tree of order \(k\geq 1\). It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary \(k\geq 2\) we...

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Bibliographic Details
Published in:arXiv.org 2012-02
Main Authors: Yu Kh Eshkabilov, Haydarov, F H, Rozikov, U A
Format: Article
Language:English
Subjects:
Integral equations
Splitting
Online Access:Get full text
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Summary:We consider models with nearest-neighbor interactions and with the set \([0,1]\) of spin values, on a Cayley tree of order \(k\geq 1\). It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary \(k\geq 2\) we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.
ISSN:2331-8422
DOI:10.48550/arxiv.1202.1722