najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-2-134-141najo-9Research ArticleMATHEMATICSМАТЕМАТИКАThe phase transition for the three-state SOS model with one-level competing interactions on the binary treeФазовый переход для трехсостоянной модели SOS с одноуровневыми конкурентными взаимодействиями на бинарном деревеhttps://orcid.org/0000-0001-6204-4621КаршибоевО. Ш.KarshiboevO. Sh.

Обид Ш. Каршибоев

Obid Sh. Karshiboev

University, 161, Boburshox str, 160107, Namangan

okarshiboevsher@mail.ruhttps://orcid.org/0000-0003-2987-7714РахматуллаевМ. М.RahmatullaevM. M.

Музаффар М. Рахматуллаев

Muzaffar M. Rahmatullaev

4-b, University str, 100174, Tashkent

100000, Tashkent

mrahmatullaev@rambler.ruNamangan State UniversityUzbekistanV. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan UniversityUzbekistan202519052025162134141Copyright © Karshiboev O.S., Rahmatullaev M.M., 20252025Каршибоев О.Ш., Рахматуллаев М.М.Karshiboev O.S., Rahmatullaev M.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/9

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.

В этой статье мы рассматриваем solid-on-solid (SOS) модель с тремя состояниями с двумя конкурирующими взаимодействиями (ближайший сосед, одноуровневый следующий ближайший сосед) на дереве Кэли второго порядка. Показано, что при некоторых значениях параметров в модели наблюдается фазовый переход. Также доказано, что для модели при некоторых условиях не существует двухпериодических мер Гиббса.

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The authors declare that there are no conflicts of interest present.