U. A. Rozikov, “Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions”, TMF, 112:1 (1997), 170–175; Theoret. and Math. Phys., 112:1 (1997), 929

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 112, Number 1, Pages 170–175
DOI: https://doi.org/10.4213/tmf1037 (Mi tmf1037)

This article is cited in 58 scientific papers (total in 58 papers)

Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Full-text PDF (204 kB) Citations (58)

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DOI: https://doi.org/10.4213/tmf1037

Abstract: The disposition order of partition elements into adjacent classes of the group representation of the Cayley tree on its finite index normal subgroups is described. For the inhomogeneous Ising model it is proved that there exist three

H_{0}

$H_0$ -periodic Gibbs distributions, where

H_{0}

$H_0$ is a normal subgroup of finite index.

Received: 05.08.1996
Revised: 16.01.1997

English version:
Theoretical and Mathematical Physics, 1997, Volume 112, Issue 1, Pages 929–933
DOI: https://doi.org/10.1007/BF02634109

Bibliographic databases:

Language: Russian

Citation: U. A. Rozikov, “Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions”, TMF, 112:1 (1997), 170–175; Theoret. and Math. Phys., 112:1 (1997), 929–933

Citation in format AMSBIB

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https://doi.org/10.4213/tmf1037

https://www.mathnet.ru/eng/tmf/v112/i1/p170

This publication is cited in the following 58 articles:

Muzaffar M. Rahmatullaev, Zulxumor A. Burxonova, “Constructive Gibbs measures for the Ising model on the Cayley tree”, Reports on Mathematical Physics, 93:3 (2024), 361
Dilshod O. Egamov, “Periodic and weakly periodic ground states corresponding to the subgroups of index three for the Ising model on the Cayley tree of order three”, Ukr. Mat. Zhurn., 75:6 (2023), 793
U. A. Rozikov, F. H. Haydarov, “A HC model with countable set of spin values: Uncountable set of Gibbs measures”, Rev. Math. Phys., 35:01 (2023)
Dilshod O. Egamov, “Periodic and Weakly Periodic Ground States Corresponding to the Subgroups of Index Three for the Ising Model on the Cayley Tree of Order Three”, Ukr Math J, 75:6 (2023), 908
U. A. Rozikov, I. A. Sattarov, A. M. Tukhtabaev, “Periodic Points of a $p$ -Adic Operator and their $p$ -Adic Gibbs Measures”, P-Adic Num Ultrametr Anal Appl, 14:S1 (2022), S30
M. M. Rahmatullaev, Zh. D. Dekhkonov, “Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order $k=2$ ”, Theoret. and Math. Phys., 206:2 (2021), 185–198
Rahmatullaev M.M. Egamov D.O. Haydarov F.H., “Periodic and Weakly Periodic Ground States Corresponding to Subgroups of Index Three For the Ising Model on Cayley Tree”, Rep. Math. Phys., 88:2 (2021), 247–257
M. M. Rakhmatullaev, Zh. D. Dekhkonov, “Suschestvovanie slabo periodicheskikh mer Gibbsa dlya modeli Izinga na dereve Keli poryadka tri”, Vladikavk. matem. zhurn., 23:4 (2021), 77–88
M.M. Rahmatullaev, D.O. Egamov, F.H. Haydarov, “Periodic and weakly periodic ground states corresponding to subgroups of index three for the ising model on cayley tree”, Reports on Mathematical Physics, 88:2 (2021), 247
Mukhamedov F.M. Rakhmatullaev M.M. Rasulova M.A., “Weakly Periodic Ground States For the Lambda-Model”, Ukr. Math. J., 72:5 (2020), 771–784
Farrukh M. Mukhamedov, Muzaffar M. Rahmatullaev, M. A. Rasulova, “Slabo periodicheskie osnovnye sostoyaniya dlya λ-modeli”, Ukr. Mat. Zhurn., 72:5 (2020)
M. A. Rasulova, “Periodic Gibbs measures for the Potts–SOS model on a Cayley tree”, Theoret. and Math. Phys., 199:1 (2019), 586–592
Yusup Kh. Eshkabilov, Shohruh D. Nodirov, “Positive fixed points of cubic operators on $\mathbb{R}^{2}$ and Gibbs measures”, Zhurn. SFU. Ser. Matem. i fiz., 12:6 (2019), 663–673
U. A. Rozikov, F. Kh. Khaidarov, “Four competing interactions for models with an uncountable set of spin values on a Cayley tree”, Theoret. and Math. Phys., 191:3 (2017), 910–923
Ganikhodjaev N. Rahmatullaev M. Rodzhan Mohd Hirzie Bin Mohd, “Weakly Periodic Gibbs Measures of the Ising Model on the Cayley Tree of Order Five and Six”, Math. Phys. Anal. Geom., 21:1 (2017), 2
Rahmatullaev M., “Ising Model on Trees: (K(0)) - Non Translation-Invariant Gibbs Measures”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, ed. Accardi L. Mukhamedov F. Hee P., IOP Publishing Ltd, 2017, UNSP 012019
Eshkabilov Yu.Kh. Nodirov Sh.D. Haydarov F.H., “Positive fixed points of quadratic operators and Gibbs measures”, Positivity, 20:4 (2016), 929–943
Eshkabilov Yu.Kh. Bobonazarov Sh.P. Teshaboev R.I., “Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree”, Nanosyst.-Phys. Chem. Math., 7:5 (2016), 893–899
Khakimov R.M., “Weakly Periodic Gibbs Measures in the HC-Model for a Normal Divisor of Index Four”, Ukr. Math. J., 67:10 (2016), 1584–1598
Gandolfo D. Rozikov U.A. Ruiz J., “on Four State Hard Core Models on the Cayley Tree”, Markov Process. Relat. Fields, 22:2 (2016), 359–377

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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