On phase transitions of the Potts model with three competing interactions on Cayley tree
In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2011
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119977 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On phase transitions of the Potts model with three competing interactions on Cayley tree / H. Akin, S. Temir // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23003:1-11. — Бібліогр.: 20 назв. — англ. |
Репозиторії
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irk-123456789-1199772017-06-11T03:02:54Z On phase transitions of the Potts model with three competing interactions on Cayley tree Akin, H. Temir, S. In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting. У цiй статтi ми вивчаємо проблему фазового переходу для моделi Поттса з трьома конкуруючими взаємодiями, найближчих сусiдiв, наступних близьких сусiдiв i наступних за наступними близькими сусiдами,з ненульовим зовнiшнiм полем на деревi Келi другого порядку. Ми доводимо, що для деяких значень параметрiв моделi є фазовий перехiд. Ми приводимо проблему опису граничних мiр Гiббса до проблеми розв’язку системи нелiнiйних функцiональних рiвнянь. Ми розширюємо результати, отриманi Ганiходяєвим i Розiковим [Math. Phys. Anal. Geom., 2009, 12, No 2, 141–156] для фазового переходу в моделi Iзiнга,на випадок моделi Поттса. 2011 Article On phase transitions of the Potts model with three competing interactions on Cayley tree / H. Akin, S. Temir // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23003:1-11. — Бібліогр.: 20 назв. — англ. 1607-324X PACS: 05.50.+q, 64.60.-i, 64.60.De, 75.10.Hk DOI:10.5488/CMP.14.23003 arXiv:math/0703699 http://dspace.nbuv.gov.ua/handle/123456789/119977 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting. |
| format |
Article |
| author |
Akin, H. Temir, S. |
| spellingShingle |
Akin, H. Temir, S. On phase transitions of the Potts model with three competing interactions on Cayley tree Condensed Matter Physics |
| author_facet |
Akin, H. Temir, S. |
| author_sort |
Akin, H. |
| title |
On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_short |
On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_full |
On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_fullStr |
On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_full_unstemmed |
On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_sort |
on phase transitions of the potts model with three competing interactions on cayley tree |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119977 |
| citation_txt |
On phase transitions of the Potts model with three competing interactions on Cayley tree / H. Akin, S. Temir // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23003:1-11. — Бібліогр.: 20 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT akinh onphasetransitionsofthepottsmodelwiththreecompetinginteractionsoncayleytree AT temirs onphasetransitionsofthepottsmodelwiththreecompetinginteractionsoncayleytree |
| first_indexed |
2023-10-18T20:35:53Z |
| last_indexed |
2023-10-18T20:35:53Z |
| _version_ |
1796150617657311232 |