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

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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 116 scientific papers (total in 116 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

Full-text PDF (253 kB) Citations (116)

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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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https://doi.org/10.4213/tmf993

https://www.mathnet.ru/eng/tmf/v111/i1/p109

This publication is cited in the following 116 articles:

B. Z. Tozhiboev, R. M. Khakimov, “Mery Gibbsa dlya $\mathrm{HC}$-modeli v sluchae grafa tipa “klyuch” na dereve Keli”, Matem. zametki, 117:4 (2025), 575–590
N. M. Khatamov, N. N. Malikov, “Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model”, Theoret. and Math. Phys., 218:2 (2024), 346–356
Rustamjon Khakimov, Kamola Umirzakova, “Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand”, Z. mat. fiz. anal. geom., 20:1 (2024), 66
U. A. Rozikov, R. M. Khakimov, M. T. Makhammadaliev, “Gibbs Periodic Measures for a Two-State HC-Model on a Cayley Tree”, J Math Sci, 278:4 (2024), 647
R. M. Khakimov, B. Z. Tozhiboev, “Gibbs measures for fertile models with hard-core interactions and four states”, Theoret. and Math. Phys., 219:2 (2024), 823–838
M. M. Rahmatullaev, B. M. Isakov, “Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree”, Theoret. and Math. Phys., 219:3 (2024), 1048–1059
Begzod Isakov, Olimkhon Akhmedov, “FUNKTsIONALNYE URAVNENIYa DLYa PREDELNYKh MER GIBBSA MODELI IZINGA-POTTSA NA DEREVE KELI”, VOGUMFT, 2024, no. 1(4), 90
Rustamjon Khakimov, Muhtorjon Makhammadaliev, Kamola Umirzakova, “Alternative Gibbs measure for fertile three-state Hard-Core models on a Cayley tree”, Phase Transitions, 2024, 1
Muhtorjon Makhammadaliev, “Weakly periodic gibbs measures for the HC model with a countable set of spin values”, Reports on Mathematical Physics, 94:1 (2024), 83
M. T. Makhammadaliev, “Pure phases of the ferromagnetic Potts model with $q$ states on the Cayley tree of order three”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:4 (2024), 499–517
M. M. Rahmatullaev, B. M. Isakov, “Ground states of Ising-Potts model on Cayley tree”, Ufa Math. J., 15:1 (2023), 43–55
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
R. M. Khakimov, M. T. Makhammadaliev, F. H. Haydarov, “New class of Gibbs measures for two-state hard-core model on a Cayley tree”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 26:04 (2023)
U. A. Rozikov, M. M. Rahmatullaev, R. M. Khakimov, “Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree”, Theoret. and Math. Phys., 210:1 (2022), 135–153
U. A. Rozikov, R. M. Khakimov, M. T. Makhammadaliev, “Periodicheskie mery Gibbsa dlya NS-modeli s dvumya sostoyaniyami na dereve Keli”, Nauka — tekhnologiya — obrazovanie — matematika — meditsina, SMFN, 68, no. 1, Rossiiskii universitet druzhby narodov, M., 2022, 95–109
J. D. Dekhkonov, “On $(k_0)$-translation-invariant and $(k_0)$-periodic Gibbs measures for Potts model on Cayley tree”, Ufa Math. J., 14:4 (2022), 42–55
H. Akιn, “Phase diagrams of lattice models on Cayley tree and chandelier network: a review”, Condens. Matter Phys., 25:3 (2022), 32501
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
Rozikov U.A., “Gibbs Measures of Potts Model on Cayley Trees: a Survey and Applications”, Rev. Math. Phys., 33:10 (2021), 2130007

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

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