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arXiv · 1202.1722

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

Yu. Kh. Eshkabilov·F. H. Haydarov·U. A. Rozikov
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Abstract

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.

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Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov. 2012-02-08. Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree. https://doi.org/10.1007/s11040-012-9118-6

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