Geodesic
Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 663-673.

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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 $\mathbb{R}_+^{2}$.
Keywords: Cayley tree, Gibbs measure, translation-invariant Gibbs measure, fixed point, cubic operator, Hammerstein's integral operator. 
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Yusup Kh. Eshkabilov; Shohruh D. Nodirov. Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 663-673. http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a1/

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