Periodic and weakly periodic ground states corresponding to the subgroups of index three for the Ising model on the Cayley tree of order three-Reference-Cited by-同舟云学术

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Periodic and weakly periodic ground states corresponding to the subgroups of index three for the Ising model on the Cayley tree of order three

Published:2023-06-20 Issue:6 Volume:75 Page:793-804
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Egamov Dilshod O.

Abstract

UDC 517.9 We determine periodic and weakly periodic ground states with subgroups of index three for the Ising model on the Cayley tree of order three.

Publisher

SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

Subject

General Earth and Planetary Sciences,General Engineering,General Environmental Science

Reference24 articles.

1. U. A. Rozikov, A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree, J. Stat. Phys., 122, 217–235 (2006).

2. R. J. Baxter, Exactly solved models in statistical mechanics, Acad. Press, London, New York (1982).

3. P. M. Bleher, J. Ruiz, V. A. Zagrebnov, On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice, J. Stat. Phys., 79, № 1, 473–482 (1995).

4. P. M. Bleher, N. N. Ganikhodjaev, On pure phases of the Ising model on the Bethe lattice, Theory Probab. and Appl., 35, 216–227 (1990).

5. P. M. Bleher, J. Ruiz, R. H. Schonmann, S. Shlosman, V. A. Zagrebnov, Rigidity of the critical phases on a Cayley tree, Moscow Math. J., 3, (2001).

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