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TMF, 1990, Volume 85, Number 2, Pages 163–175 (Mi tmf5939)  

This article is cited in 37 scientific papers (total in 37 papers)

Pure phases of the ferromagnetic Potts model with three states on a second-order Bethe lattice

N. N. Ganikhodzhaev


Abstract: Recursion relations are obtained for the ferromagnetic Potts model with three states on a second-order Bethe lattice. It is shown that for $T<T_c$ there exists an uncountable number of pure phases, and a constructive description of these phases is given.

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English version:
Theoretical and Mathematical Physics, 1990, 85:2, 1125–1134

Bibliographic databases:

Received: 18.04.1990

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

Citation in format AMSBIB
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\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://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990FU79200001}


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

    This publication is cited in the following articles:
    1. N. N. Ganikhodzhaev, U. A. Rozikov, “Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree”, Theoret. and Math. Phys., 111:1 (1997), 480–486  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. U. A. Rozikov, “Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model”, Theoret. and Math. Phys., 118:1 (1999), 77–84  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Ganikhodjaev, N, “On disordered phase in the ferromagnetic Potts model on the Bethe lattice”, Osaka Journal of Mathematics, 37:2 (2000), 373  mathscinet  isi
    4. U. A. Rozikov, Sh. A. Shoyusupov, “Gibbs measures for the SOS model with four states on a Cayley tree”, Theoret. and Math. Phys., 149:1 (2006), 1312–1323  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Ganikhodjaev, N, “On the three state Potts model with competing interactions on the Bethe lattice”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P08012  crossref  isi
    6. Rozikov, UA, “Gibbs measures for SOS models on a Cayley tree”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 9:3 (2006), 471  crossref  mathscinet  zmath  isi
    7. Mukhamedov, F, “On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree”, Journal of Mathematical Physics, 48:1 (2007), 013301  crossref  mathscinet  zmath  adsnasa  isi
    8. Rozikov, UA, “A contour method on Cayley trees”, Journal of Statistical Physics, 130:4 (2008), 801  crossref  mathscinet  zmath  adsnasa  isi
    9. Gandolfo D., Rozikov U.A., Ruiz J., “On P-Adic Gibbs Measures for Hard Core Model on a Cayley Tree”, Markov Process. Relat. Fields, 18:4 (2012), 701–720  isi
    10. Mukhamedov F., “A Dynamical System Approach to Phase Transitions for P-Adic Potts Model on the Cayley Tree of Order Two”, Rep. Math. Phys., 70:3 (2012), 385–406  isi
    11. Eshkabilov Y.K., Haydarov F.H., Rozikov U.A., “Non-Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree”, J. Stat. Phys., 147:4 (2012), 779–794  crossref  isi
    12. U. A. Rozikov, R. M. Khakimov, “Periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 175:2 (2013), 699–709  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. F. M. Mukhamedov, H. Akin, “The $p$-adic Potts model on the Cayley tree of order three”, Theoret. and Math. Phys., 176:3 (2013), 1267–1279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. O. N. Khakimov, “$p$-Adic Gibbs measures for the hard core model with three states on the Cayley tree”, Theoret. and Math. Phys., 177:1 (2013), 1339–1351  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  isi
    16. Mukhamedov F., Akin H., “Phase Transitions for P-Adic Potts Model on the Cayley Tree of Order Three”, J. Stat. Mech.-Theory Exp., 2013, P07014  crossref  isi
    17. Eshkabilov Yu.Kh., Haydarov F.H., Rozikov U.A., “Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree”, Math. Phys. Anal. Geom., 16:1 (2013), 1–17  crossref  isi
    18. Mukhamedov F., “On Dynamical Systems and Phase Transitions for Q+1-State P-Adic Potts Model on the Cayley Tree”, Math. Phys. Anal. Geom., 16:1 (2013), 49–87  crossref  isi
    19. R. M. Khakimov, “Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree”, Theoret. and Math. Phys., 179:1 (2014), 405–415  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Rustamjon M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, Zhurn. SFU. Ser. Matem. i fiz., 7:3 (2014), 297–304  mathnet
    21. M. M. Rakhmatullaev, “The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 180:3 (2014), 1019–1029  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    22. N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 836–845  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. M. M. Rahmatullaev, “A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree”, Siberian Math. J., 56:5 (2015), 929–935  mathnet  crossref  crossref  isi  elib
    24. R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 189:2 (2016), 1651–1659  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. M. M. Rahmatullaev, “On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree”, Zhurn. matem. fiz., anal., geom., 12:4 (2016), 302–314  mathnet  crossref  mathscinet
    26. Eshkabilov Yu.Kh., Nodirov Sh.D., Haydarov F.H., “Positive fixed points of quadratic operators and Gibbs measures”, Positivity, 20:4 (2016), 929–943  crossref  mathscinet  zmath  isi  scopus
    27. 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  crossref  isi
    28. Rakhmatullaev M.M., “On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree”, Ukr. Math. J., 68:4 (2016), 598–611  crossref  mathscinet  isi  scopus
    29. Haydarov F., Khakimov R., “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. Ayupov S., Chilin V., Ganikhodjaev N., Mukhamedov F., Rakhimov I., IOP Publishing Ltd, 2016, 012019  crossref  isi  scopus
    30. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. 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  crossref  isi
    32. F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the $\lambda$ model on the Cayley tree”, Theoret. and Math. Phys., 194:2 (2018), 260–273  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    33. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    34. 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  crossref  isi
    35. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    36. 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  mathnet  crossref
    37. 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  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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