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Mat. Sb., 1999, Volume 190, Number 2, Pages 31–42 (Mi msb382)  

This article is cited in 8 scientific papers (total in 8 papers)

On unordered phases of certain models on a Cayley tree

N. N. Ganikhodzhaev, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Ising model with several spin values, the Potts model, and the inhomogeneous Ising model. For each model we prove sufficiency conditions for extremality of the unordered phase.

DOI: https://doi.org/10.4213/sm382

Full text: PDF file (248 kB)
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English version:
Sbornik: Mathematics, 1999, 190:2, 193–203

Bibliographic databases:

UDC: 517.2+530.1
MSC: 82B20
Received: 16.03.1998

Citation: N. N. Ganikhodzhaev, U. A. Rozikov, “On unordered phases of certain models on a Cayley tree”, Mat. Sb., 190:2 (1999), 31–42; Sb. Math., 190:2 (1999), 193–203

Citation in format AMSBIB
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\paper On unordered phases of certain models on a~Cayley tree
\jour Mat. Sb.
\yr 1999
\vol 190
\issue 2
\pages 31--42
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\jour Sb. Math.
\yr 1999
\vol 190
\issue 2
\pages 193--203
\crossref{https://doi.org/10.1070/sm1999v190n02ABEH000382}
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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. F. M. Mukhamedov, U. A. Rozikov, “The disordered phase of the inhomogeneous Potts model is extremal on the Cayley tree”, Theoret. and Math. Phys., 124:3 (2000), 1202–1210  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. U. A. Rozikov, “Periodic Gibbs measures of the inhomogeneous Ising model on trees”, Russian Math. Surveys, 56:1 (2001), 172–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. F. M. Mukhamedov, U. A. Rozikov, “Von Neumann algebra corresponding to one phase of the inhomogeneous Potts model on a Cayley tree”, Theoret. and Math. Phys., 126:2 (2001), 169–174  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. M. Rakhmatullaev, U. A. Rozikov, “Gibbs Measures and Markov Random Fields with Association $I$”, Math. Notes, 72:1 (2002), 83–89  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. U. A. Rozikov, “Representability of Trees and Some of Their Applications”, Math. Notes, 72:4 (2002), 479–488  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. U. A. Rozikov, “Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree”, Theoret. and Math. Phys., 130:1 (2002), 92–100  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. 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 $\mathbb {Z}$”, Theoret. and Math. Phys., 130:3 (2002), 425–431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. N. N. Ganikhodzhaev, U. A. Rozikov, “Group representation of the Cayley forest and some of its applications”, Izv. Math., 67:1 (2003), 17–27  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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