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TMF, 2002, Volume 130, Number 3, Pages 493–499 (Mi tmf314)  

This article is cited in 9 scientific papers (total in 9 papers)

Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions

N. N. Ganikhodzhaev

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: The exact solution is found for the problem of phase transitions in the Ising model with competing ternary and binary interactions. For the pair of parameters $\theta =\theta (J)$ and $\theta _1=\theta _1(J_1)$ in the plane $(\theta _1,\theta )$, we find two critical curves such that a phase transition occurs for all pairs $(\theta _1,\theta )$ lying between the curves.


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English version:
Theoretical and Mathematical Physics, 2002, 130:3, 419–424

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Received: 23.02.2001
Revised: 08.10.2001

Citation: N. N. Ganikhodzhaev, “Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions”, TMF, 130:3 (2002), 493–499; Theoret. and Math. Phys., 130:3 (2002), 419–424

Citation in format AMSBIB
\by N.~N.~Ganikhodzhaev
\paper Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions
\jour TMF
\yr 2002
\vol 130
\issue 3
\pages 493--499
\jour Theoret. and Math. Phys.
\yr 2002
\vol 130
\issue 3
\pages 419--424

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    This publication is cited in the following articles:
    1. Ganikhodjaev NN, Pah CH, Wahiddin MRB, “An Ising model with three competing interactions on a Cayley tree”, Journal of Mathematical Physics, 45:9 (2004), 3645–3658  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Mukhamedov F, Rozikov U, “On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras”, Journal of Statistical Physics, 114:3–4 (2004), 825–848  crossref  mathscinet  zmath  adsnasa  isi
    3. N. N. Ganikhodzhaev, C. H. Pah, “Phase diagrams of multicomponent lattice models”, Theoret. and Math. Phys., 149:2 (2006), 1512–1518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Ganikhodjaev, NN, “On Ising Model with Four Competing Interactions on Cayley Tree”, Mathematical Physics Analysis and Geometry, 12:2 (2009), 141  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Strecka J., “Generalized algebraic transformations and exactly solvable classical-quantum models”, Phys Lett A, 374:36 (2010), 3718–3722  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus  scopus
    7. bin Ali R., Mukhamedov F., Pah Ch.H., “Ising Model with Competing Interactions on Cayley Tree of Order 4: an Analytic Solution”, International Conference on Advancement in Science and Technology 2012 (Icast): Contemporary Mathematics, Mathematical Physics and their Applications, Journal of Physics Conference Series, 435, eds. Ganikhodjaev N., Mukhamedov F., Hee P., IOP Publishing Ltd, 2013  crossref  isi  scopus  scopus
    8. Jamil H., Pah Ch.H., “Exact solution for an Ising model on the Cayley tree of order 5”, ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23) (Johor Bahru, Malaysia, 24?26 November 2015), AIP Conference Proceedings, 1750, eds. Salleh S., Aris N., Bahar A., Zainuddin Z., Maan N., Lee M., Ahmad T., Yusof Y., Amer Inst Physics, 2016, 020011  crossref  isi  scopus
    9. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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