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TMF, 1977, Volume 33, Number 1, Pages 110–118 (Mi tmf3208)  

This article is cited in 5 scientific papers (total in 5 papers)

Structure of ground states in three-dimensional using model with three-step interaction

I. A. Kashapov


Abstract: The recent work [1] by S.  A. Pirogov and Ya.  G. Sinay investigated the phase diagrams for classical lattice systems with finite number of ground states, which satisfy a certain stability condition. This condition was called the Payerls condition in the work [1]. For corresponding Hamiltonians it was proved that the structure of the phase diagrams is determined by the structure of ground states. Thus the problem of studying the phase diagrams was reduced to the problem of investigating the ground states of the original Hamiltonians. Structure of ground states for three-dimensional Ising model with the two-step interaction is given in the work [2] by V.  M. Gertsik and R.  L. Dobrushin. The present work investigates the structure of ground states and tests the Payerls condition for certain Hamiltonians of the Ising type. Some generalizations are presented in the last section of the paper.

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English version:
Theoretical and Mathematical Physics, 1977, 33:1, 912–918

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Received: 07.02.1977

Citation: I. A. Kashapov, “Structure of ground states in three-dimensional using model with three-step interaction”, TMF, 33:1 (1977), 110–118; Theoret. and Math. Phys., 33:1 (1977), 912–918

Citation in format AMSBIB
\Bibitem{Kas77}
\by I.~A.~Kashapov
\paper Structure of ground states in three-dimensional using model with three-step interaction
\jour TMF
\yr 1977
\vol 33
\issue 1
\pages 110--118
\mathnet{http://mi.mathnet.ru/tmf3208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=456168}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 33
\issue 1
\pages 912--918
\crossref{https://doi.org/10.1007/BF01039015}


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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. Rozikov, UA, “A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree”, Journal of Statistical Physics, 122:2 (2006), 217  crossref  isi
    2. G. I. Botirov, U. A. Rozikov, “Potts model with competing interactions on the Cayley tree: The contour method”, Theoret. and Math. Phys., 153:1 (2007), 1423–1433  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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  isi
    4. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  isi
    5. N. M. Khatamov, “New classes of ground states for the Potts model with random competing interactions on a Cayley tree”, Theoret. and Math. Phys., 180:1 (2014), 827–834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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