Abstract:
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.
Received: 13.03.2019 Received in revised form: 16.04.2019 Accepted: 10.07.2019
Bibliographic databases:
Document Type:
Article
UDC:517.98+530.1
Language: English
Citation:
Yusup Kh. Eshkabilov, Shohruh D. Nodirov, “Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures”, J. Sib. Fed. Univ. Math. Phys., 12:6 (2019), 663–673
\Bibitem{EshNod19}
\by Yusup~Kh.~Eshkabilov, Shohruh~D.~Nodirov
\paper Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 6
\pages 663--673
\mathnet{http://mi.mathnet.ru/jsfu802}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-6-663-673}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000501590600002}
Linking options:
https://www.mathnet.ru/eng/jsfu802
https://www.mathnet.ru/eng/jsfu/v12/i6/p663
This publication is cited in the following 2 articles:
I. M. Mavlonov, N. Kh. Khushvaktov, G. P. Arzikulov, F. Kh. Khaidarov, “On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs measures”, Theoret. and Math. Phys., 220:3 (2024), 1580–1588
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