The phase transition for the three-state SOS model with one-level competing interactions on the binary tree
https://doi.org/10.17586/2220-8054-2025-16-2-134-141
Abstract
In this paper, we consider a three-state solid-on-solid (SOS) model with two competing interactions (nearest-neighbor, one-level next-nearest-neighbor) on the Cayley tree of order two. We show that at some values of the parameters the model exhibits a phase transition. We also prove that for the model under some conditions there is no two-periodic Gibbs measures.
Supporting agencies: The second author (MMR) thanks the State Grant F-FA-2021-425 of the Republic of Uzbekistan. We thank the referee for the careful reading of the manuscript and especially for a number of suggestions that have improved the paper.
About the Authors
O. Sh. Karshiboev
Namangan State University
Uzbekistan
Uzbekistan
Obid Sh. Karshiboev
University, 161, Boburshox str, 160107, Namangan
M. M. Rahmatullaev
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University
Uzbekistan
Uzbekistan
Muzaffar M. Rahmatullaev
4-b, University str, 100174, Tashkent
100000, Tashkent
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Review
For citations:
Karshiboev O.Sh., Rahmatullaev M.M. The phase transition for the three-state SOS model with one-level competing interactions on the binary tree. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(2):134-141. https://doi.org/10.17586/2220-8054-2025-16-2-134-141
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