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Tr. Mat. Inst. Steklova, 2009, Volume 265, Pages 177–188 (Mi tm833)  

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

On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model

F. Mukhamedov

Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Kuantan, Pahang, Malaysia

Abstract: We consider the one-dimensional countable state $p$-adic Potts model. A construction of generalized $p$-adic Gibbs measures depending on weights $\lambda$ is given, and an investigation of such measures is reduced to the examination of a $p$-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized $p$-adic Gibbs measures. Note that the condition found does not depend on the values of the prime $p$, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 165–176

Bibliographic databases:

UDC: 531.19
Received in June 2008
Language:

Citation: F. Mukhamedov, “On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Tr. Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 177–188; Proc. Steklov Inst. Math., 265 (2009), 165–176

Citation in format AMSBIB
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\paper On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model
\inbook Selected topics of mathematical physics and $p$-adic analysis
\bookinfo Collected papers
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\yr 2009
\vol 265
\pages 177--188
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. 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
    2. 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  mathscinet  zmath  isi
    3. Mukhamedov F., “Existence of P-Adic Quasi Gibbs Measure for Countable State Potts Model on the Cayley Tree”, J. Inequal. Appl., 2012, 104  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. 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
    6. 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
    7. 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
    8. Mukhamedov F., Akin H., “on Non-Archimedean Recurrence Equations and Their Applications”, J. Math. Anal. Appl., 423:2 (2015), 1203–1218  crossref  mathscinet  zmath  isi  elib  scopus
    9. Rozikov U.A., Khakimov O.N., “Description of All Translation-Invariant P-Adic Gibbs Measures For the Potts Model on a Cayley Tree”, Markov Process. Relat. Fields, 21:1 (2015), 177–204  mathscinet  zmath  isi  elib
    10. Mukhamedov F., Khakimov O., “on a Generalized Self-Similarity in the P-Adic Field”, Fractals-Complex Geom. Patterns Scaling Nat. Soc., 24:4 (2016), 1650041  crossref  zmath  isi  scopus
    11. Mukhamedov F., Khakimov O., “Phase transition and chaos: P-adic Potts model on a Cayley tree”, Chaos Solitons Fractals, 87 (2016), 190–196  crossref  mathscinet  zmath  isi  elib  scopus
    12. U. A. Rozikov, Z. T. Tugyonov, “Construction of a set of $p$-adic distributions”, Theoret. and Math. Phys., 193:2 (2017), 1694–1702  mathnet  crossref  crossref  adsnasa  isi  elib
    13. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    14. F. M. Mukhamedov, O. N. Khakimov, “$p$-adic monomial equations and their perturbations”, Izv. Math., 84:2 (2020), 348–360  mathnet  crossref  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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