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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 111, Number 1, Pages 109–117
DOI: https://doi.org/10.4213/tmf993 (Mi tmf993) 		 
This article is cited in 114 scientific papers (total in 114 papers)

Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree

N. N. Ganikhodzhaev, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
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DOI: https://doi.org/10.4213/tmf993
Abstract: It is proved that the translational invariant extreme Gibbs measure is unique for the antiferromagnetic Potts model with the external field. The existence of uncountable numbers of the extreme Gibbs measures for the Ising model with the external field on the Cayley tree is proved. The classes of normal subgroups of finite index of group representation of the Cayley tree is constructed. The periodic extreme Gibbs measures invariant with respect to subgroups of index two for the Ising model are constructed and the existence of uncountable numberes of the nonperiodic extreme Gibbs measures for the antiferromagnetic Ising model is proved.
Received: 16.04.1996
English version:
Theoretical and Mathematical Physics, 1997, Volume 111, Issue 1, Pages 480–486
DOI: https://doi.org/10.1007/BF02634202
Bibliographic databases:
Language: Russian
Citation: N. N. Ganikhodzhaev, U. A. Rozikov, “Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree”, TMF, 111:1 (1997), 109–117; Theoret. and Math. Phys., 111:1 (1997), 480–486
Citation in format AMSBIB
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\paper Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree
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\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 111
\issue 1
\pages 480--486
\crossref{https://doi.org/10.1007/BF02634202}
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    • This publication is cited in the following 114 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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