Translation-invariant Gibbs measures of a model on Cayley tree

Authors

Golibjon Botirov, National University of UzbekistanFollow

Abstract

We consider a model where the spin takes values in the set [0,1]^d, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.

First Page

36

Last Page

42

References

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Recommended Citation

Botirov, Golibjon (2018) "Translation-invariant Gibbs measures of a model on Cayley tree," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 1: Iss. 2, Article 1.
DOI: https://doi.org/10.56017/2181-1318.1011