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TMF, 2002, Volume 130, Number 3, Pages 500–507 (Mi tmf315)  

This article is cited in 14 scientific papers (total in 14 papers)

$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$

N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Potts model on the set $\mathbb {Z}$ in the field $Q_p$ of $p$-adic numbers. The range of the spin variables $\sigma (n)$, $n\in \mathbb Z$, in this model is $\Phi =\{\sigma _1,\sigma _2,……,\sigma _q\}\subset Q_p^{q-1}=\underbrace {Q_p\times Q_p\times …\times Q_p}_{q-1}$. We show that there are some values $q=q(p)$ for which phase transitions.

DOI: https://doi.org/10.4213/tmf315

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English version:
Theoretical and Mathematical Physics, 2002, 130:3, 425–431

Bibliographic databases:

Received: 24.01.2001
Revised: 20.06.2001

Citation: N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, TMF, 130:3 (2002), 500–507; Theoret. and Math. Phys., 130:3 (2002), 425–431

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khamraev M, Mukhamedov F, “On p-adic lambda-model on the Cayley tree”, Journal of Mathematical Physics, 45:11 (2004), 4025–4034  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Mukhamedov FM, Rozikov UA, “On Gibbs measures of P-adic Potts model on the cayley tree”, Indagationes Mathematicae-New Series, 15:1 (2004), 85–99  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Khamraev M, Mukhamedov F, Rozikov U, “On the uniqueness of Gibbs measures for p-adic nonhomogeneous lambda-model on the Cayley tree”, Letters in Mathematical Physics, 70:1 (2004), 17–28  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Mukhamedov, F, “On inhomogeneous (p)-adic Potts model on a Cayley tree”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 8:2 (2005), 277  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Khamraev, M, “On a class of rational p-adic dynamical systems”, Journal of Mathematical Analysis and Applications, 315:1 (2006), 76  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. F. M. Mukhamedov, U. A. Rozikov, “A polynomial $p$-adic dynamical system”, Theoret. and Math. Phys., 170:3 (2012), 376–383  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    7. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    8. Albeverio S. Rozikov U.A. Sattarov I.A., “P-Adic (2,1)-Rational Dynamical Systems”, J. Math. Anal. Appl., 398:2 (2013), 553–566  crossref  mathscinet  zmath  isi  elib  scopus
    9. 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
    10. 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  mathscinet  isi  elib  scopus  scopus
    11. 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  mathscinet  zmath  isi  elib  scopus  scopus
    12. Mukhamedov F., “On the Strong Phase Transition For the One-Dimensional Countable State P-Adic Potts Model”, J. Stat. Mech.-Theory Exp., 2014, P01007  crossref  mathscinet  isi  scopus  scopus
    13. Saburov M., Ahmad Mohd Ali Khameini, “The Dynamics of the Potts-Bethe Mapping Over Q(P) the Case P Equivalent to 2 (Mod 3)”, 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 012017  crossref  mathscinet  isi  scopus  scopus
    14. Ahmad Mohd Ali Khameini Liao L. Saburov M., “Periodic P-Adic Gibbs Measures of Q-State Potts Model on Cayley Trees i: the Chaos Implies the Vastness of the Set of P-Adic Gibbs Measures”, J. Stat. Phys., 171:6 (2018), 1000–1034  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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