najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-2-153-164najo-1755Research ArticleMATHEMATICSМАТЕМАТИКАWeakly periodic measure and phase transition: q-state p-adic Potts model on the Cayley tree of order kСлабо периодическая мера и фазовый переход: q-состояния и p-адическая модель Поттса на дереве Кэли порядка khttps://orcid.org/0000-0001-8855-9199ТухтабаевА. М.TukhtabaevA. M.

Akbarkhuja M. Tukhtabaev 

P.O. Box, 160107, 161 Boburshoh street, Namangan 

75 A Chortoq street, Namangan 

akbarxoja.toxtaboyev@mail.ruNamangan State University ; Kimyo International University in Tashkent Branch NamanganUzbekistan202630042026172153164Copyright © Tukhtabaev A.M., 20262026Тухтабаев А.М.Tukhtabaev A.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/1755

In this paper, we investigate weakly periodic p-adic quasi Gibbs measures for the q-state Potts model on the Cayley tree of order k. Furthermore, we demonstrate that for all q ≥ 3 and k ≥ 2, there exist a prime number p and a parameter θ that guarantee the occurrence of a phase transition.

В данной работе исследуются слабо периодические p-адические квазигиббсовские меры для модели Поттса с q состояниями на дереве Кэли порядка k. Кроме того, продемонстрировано, что для всех q, не меньших 3, и k, не меньших 2, существуют такое простое число p и параметр, которые гарантируют возникновение фазового перехода.

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