On periodic ground states for the Chui-Weeks model
In this paper, we consider the three-state Chui–Weeks model on the Cayley tree of arbitrary order
not less than four. For this model, all translation-invariant and all periodic ground states with respect
to any normal divisor of index two are described.
1. Abraev B.U. On weakly periodic ground states for the SOS model. Scientific Bulletin of Namangan State
University, 2020, V.2, No. 3, pp. 14–21.
2. Cuesta, Jose A., Sanchez A. General non-existence theorem for phase transitions in one-dimensional
systems with short range interactions, and physical examples of such transitions. Journal of Statistical
Physics, 2004, V.115, Issue 3, pp. 869–893.
3. Ganikhodzhaev N.N. Group representation and automorphisms of the Cayley tree. Dokl. Akad. Nauk
Resp. Uzbekistan, 1994, Issue 4, pp. 3–5.
4. Rahmatullaev M.M., Abdusalomova M.R., Rasulova M.A. Ground states for the SOS model with an
external field on the Cayley tree. Uzbek Mathematical Journal, 2020, No. 2, pp. 145–156.
5. Rahmatullaev M.M., Rasulova M.A. Ground States and Gibbs Measures for the Potts-SOS Model
with an External Field on the Cayley Tree. Lobachevskii Journal of Mathematics, 2024. DOI:
10.1134/S1995080224010451.
6. Rahmatullaev M.M., Rasulova M.A., Hakimova M.A. Periodic ground states for the Chui-Weeks model
on the Cayley tree of order two. Acta NUUz: Exact Sciences, 2024, 2/2.1, pp. 104–110.
7. Rasulova M.A., Hakimova M.A. Periodic Ground States for the Chui-Weeks Model on the Cayley Tree of
Order Three. Letters in Mathematical Physics [accepted].
8. Rozikov U.A. Gibbs measures on Cayley trees. World scientific, Singapore, 2013. DOI: 10.1142/8841.
9. Rozikov U.A. Gibbs Measures in Biology and Physics: The Potts Model. World Scientific, Singapore, 2023.
DOI: 10.1142/12694.
10. Rozikov U.A. On q-component models on Cayley tree: contour method. Letters in Mathematical Physics,
2005. DOI: 10.1007/s11005-004-5117-2.
11. Rozikov U.A. A Contour method on Cayley trees. Journal of Statistical Physics, 2008. DOI:
10.1007/s10955-007-9455-1.
Copyright (c) 2025 «ACTA NUUz»
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
.jpg)
1.png)
