MATHEMATICS

The phase transition for the three-state SOS model with one-level competing interactions on the binary tree

Obid Sh. Karshiboev^a, Muzaffar M. Rahmatullaev<sup>bc

a</sup> Namangan State University, Namangan, Uzbekistan
^b V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
^c New Uzbekistan University, Tashkent, Uzbekistan

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.

Keywords: cayley tree, Gibbs measure, SOS model, competing interactions.

Received: 12.09.2024
Revised: 22.02.2025
Accepted: 23.02.2025

Language: English

DOI: 10.17586/2220-8054-2025-16-2-134-141