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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{JSFU_2019_12_6_a1,
     author = {Yusup Kh. Eshkabilov and Shohruh D. Nodirov},
     title = {Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and {Gibbs} measures},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {663--673},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a1/}
}
TY  - JOUR
AU  - Yusup Kh. Eshkabilov
AU  - Shohruh D. Nodirov
TI  - Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 663
EP  - 673
VL  - 12
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a1/
LA  - en
ID  - JSFU_2019_12_6_a1
ER  - 
%0 Journal Article
%A Yusup Kh. Eshkabilov
%A Shohruh D. Nodirov
%T Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 663-673
%V 12
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a1/
%G en
%F JSFU_2019_12_6_a1
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/