Трансляционно-инвариантные меры Гиббса для смешанной модели Изинга со спинами 1/2 и 1 с внешним полем на дереве Кэли
https://doi.org/10.17586/2220-8054-2024-15-5-576-585
Аннотация
Фазовые переходы смешанной модели Изинга со спинами 1/2 и 1 при наличии внешнего поля на дереве Кэли произвольной степени исследуются в рамках древовидно-индексированных цепей Маркова. Получены условия, гарантирующие существование не менее трех трансляционно-инвариантных мер Гиббса для модели на дереве Кэли порядка k. Для модели на бинарном дереве (k=2) при определенном значении внешнего поля найдено точное решение. Основное внимание уделено анализу структуры множества мер Гиббса. Определены области экстремальности и неэкстремальности неупорядоченной фазы модели на бинарном дереве.
Об авторах
Музаффар М. Рахматуллаев
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University; Namangan state University
Узбекистан
Узбекистан
Дилшод О. Эгамов
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; Namangan state University
Узбекистан
Узбекистан
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Рецензия
Для цитирования:
Рахматуллаев М.М., Эгамов Д.О. Трансляционно-инвариантные меры Гиббса для смешанной модели Изинга со спинами 1/2 и 1 с внешним полем на дереве Кэли. Наносистемы: физика, химия, математика. 2024;15(5):576-585. https://doi.org/10.17586/2220-8054-2024-15-5-576-585
For citation:
Rahmatullaev M.M., Egamov D.O. Translation-invariant Gibbs measures for the mixed spin-1/2 and spin-1 Ising model with an external field on a Cayley tree. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(5):576-585. https://doi.org/10.17586/2220-8054-2024-15-5-576-585
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