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.
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
\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://mathscinet.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}
Linking options:
https://www.mathnet.ru/eng/tmf3208
https://www.mathnet.ru/eng/tmf/v33/i1/p110
This publication is cited in the following 10 articles:
Farrukh Mukhamedov, Muzaffar M. Rahmatullaev, Dilshodbek O. EgAMOV, “Periodic ground states for the mixed spin ising model with competing interactions on a Cayley tree”, Reports on Mathematical Physics, 91:3 (2023), 379
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
Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001
Gibbs Measures and Phase Transitions, 2011, 495
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
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
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
G I Botirov, U A Rozikov, “Onq-component models on the Cayley tree: the general case”, J. Stat. Mech., 2006:10 (2006), P10006
U A Rozikov, “On q-Component Models on Cayley Tree: Contour Method”, Lett Math Phys, 71:1 (2005), 27
Citation in format AMSBIB
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