najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1519Research ArticleMATHEMATICSМАТЕМАТИКАPhase Transition and Thermodynamic Properties of the Hard-Core-Potts ModelKhakimovRustamjon M.rustam7102@rambler.ruhttps://orcid.org/0009-0001-6388-1322MakhammadalievMuhtorjon T.mmtmuxtor93@mail.ruMutallievNodirbek N.nodirbekmutalliyev95@gmail.comInstitute of mathematics named after V.I.RomanovskyUzbekistanNamangan state UniversityUzbekistanNamangan State Technical UniversityUzbekistan2026050320261711519Copyright © Khakimov R.M., Makhammadaliev M.T., Mutalliev N.N., 20262026Khakimov R.M., Makhammadaliev M.T., Mutalliev N.N.Khakimov R.M., Makhammadaliev M.T., Mutalliev N.N.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/1519

In this paper, Gibbs measures of the Hard-Core-Potts model on the Cayley tree are studied. The model unifies magnetic ordering and exclusion effects, providing a framework for describing phase transitions. For the hinge-type graph, the cases $k = 2$ and $k = 3$ are analyzed, and the corresponding critical parameters are determined. Thermodynamic analysis shows that the system exhibits ordered (ferromagnetic) phases at low temperatures and disordered (paramagnetic) phases at high temperatures. The results reveal the interrelation between magnetic and structural phase transitions.

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