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

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

Bibliographic databases:

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
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001
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
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