Positive Fixed Points of Cubic Operators on R² and Gibbs Measures

One model with nearest neighbour interactions of spins with values from the set [0; 1] on the Cayley tree of order three is considered in the paper. Translation-invariant Gibbs measures for the model are studied. Results are proved by using properties of the positive fixed points of a cubic operator...

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Bibliographic Details
Published in:Journal of Siberian Federal University. Mathematics & Physics 2019-12, Vol.12 (6), p.663-673
Main Authors: Eshkabilov, Yusup Kh, Nodirov, Shohruh D.
Format: Article
Language:English
Subjects:
Eigenvalues
Fixed points (mathematics)
Integral equations
Phase transitions
Statistical physics
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Summary:One model with nearest neighbour interactions of spins with values from the set [0; 1] on the Cayley tree of order three is considered in the paper. Translation-invariant Gibbs measures for the model are studied. Results are proved by using properties of the positive fixed points of a cubic operator in the cone R²₊
ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2019-12-6-663-673