Abstract:
Recursion relations are obtained for the ferromagnetic Potts model with three states on a second-order Bethe lattice. It is shown that for T<TcT<Tc there exists an uncountable number of pure phases, and a constructive description of these phases is given.
Citation:
N. N. Ganikhodzhaev, “Pure phases of the ferromagnetic Potts model with three states on a second-order Bethe lattice”, TMF, 85:2 (1990), 163–175; Theoret. and Math. Phys., 85:2 (1990), 1125–1134
\Bibitem{Gan90}
\by N.~N.~Ganikhodzhaev
\paper Pure phases of~the ferromagnetic Potts model with three states on~a~second-order Bethe lattice
\jour TMF
\yr 1990
\vol 85
\issue 2
\pages 163--175
\mathnet{http://mi.mathnet.ru/tmf5939}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1090073}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 85
\issue 2
\pages 1125--1134
\crossref{https://doi.org/10.1007/BF01086840}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990FU79200001}
Linking options:
https://www.mathnet.ru/eng/tmf5939
https://www.mathnet.ru/eng/tmf/v85/i2/p163
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Mukhamedov F., “Extremality of Disordered Phase of Lambda-Model on Cayley Trees”, Algorithms, 15:1 (2022), 18
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H. Akιn, “Phase diagrams of lattice models on Cayley tree and chandelier network: a review”, Condens. Matter Phys., 25:3 (2022), 32501
Rozikov U.A., “Gibbs Measures of Potts Model on Cayley Trees: a Survey and Applications”, Rev. Math. Phys., 33:10 (2021), 2130007
Rahmatullaev M.M., Rafikov F.K., Azamov Sh.Kh., “On the Constructive Description of Gibbs Measures For the Potts Model on a Cayley Tree”, Ukr. Math. J., 73:7 (2021), 1092–1106
M. Rahmatullaev, F. K. Rafikov, Sh. Kh. Azamov, “Pro konstruktivnі opisi mіr Gіbbsa dlya modelі Pottsa na derevі Kelі”, Ukr. Mat. Zhurn., 73:7 (2021), 938
Mukhamedov F. Pah Ch.H. Jamil H. Rahmatullaev M., “On Ground States and Phase Transition For Lambda-Model With the Competing Potts Interactions on Cayley Trees”, Physica A, 549 (2020), 124184
R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735
Yusup Kh. Eshkabilov, Shohruh D. Nodirov, “Positive fixed points of cubic operators on R2 and Gibbs measures”, Zhurn. SFU. Ser. Matem. i fiz., 12:6 (2019), 663–673
F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the λ model on the Cayley tree”, Theoret. and Math. Phys., 194:2 (2018), 260–273
U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058
Mukhamedov F., Pah Ch.H., Jamil H., “Lambda-Model With Competing Potts Interactions on Cayley Tree of Order 2”, AIP Conference Proceedings, 2013, eds. Zin S., Abdullah N., Khazali K., Roslan N., Rusdi N., Saad R., Yazid N., Zain N., Amer Inst Physics, 2018, 020032
U. A. Rozikov, M. M. Rakhmatullaev, “Free energies of the Potts model on a Cayley tree”, Theoret. and Math. Phys., 190:1 (2017), 98–108
Mukhamedov F., Pah Ch.H., Jamil H., “On Ground States of Lambda-Model on the Cayley Tree of Order Two”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, eds. Accardi L., Mukhamedov F., Hee P., IOP Publishing Ltd, 2017, UNSP 012020
Christof Külske, Utkir A. Rozikov, “Fuzzy transformations and extremality of Gibbs measures for the potts model on a Cayley tree”, Random Struct. Alg., 50:4 (2017), 636
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