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...
Saved in:
| Published in: | Condensed Matter Physics |
|---|---|
| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/119977 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749479531184128 |
|---|---|
| author | Akin, H. Temir, S. |
| author_facet | Akin, H. Temir, S. |
| 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. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| 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.
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.
|
| first_indexed | 2025-12-07T21:00:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-119977 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T21:00:25Z |
| publishDate | 2011 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Akin, H. Temir, S. 2017-06-10T15:30:06Z 2017-06-10T15:30:06Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/119977 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. The authors would like to thank Prof. Dr. N.N. Ganikhodjaev and Prof. Dr. Utkir Rozikov for valuable support and suggestions. We are also grateful to anonymous referees whose comments greatly improved the paper. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics On phase transitions of the Potts model with three competing interactions on Cayley tree До фазових переходiв моделi Поттса з трьома конкуруючими взаємодiями на деревi Келi Article published earlier |
| spellingShingle | On phase transitions of the Potts model with three competing interactions on Cayley tree Akin, H. Temir, S. |
| title | On phase transitions of the Potts model with three competing interactions on Cayley tree |
| title_alt | До фазових переходiв моделi Поттса з трьома конкуруючими взаємодiями на деревi Келi |
| 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119977 |
| work_keys_str_mv | AT akinh onphasetransitionsofthepottsmodelwiththreecompetinginteractionsoncayleytree AT temirs onphasetransitionsofthepottsmodelwiththreecompetinginteractionsoncayleytree AT akinh dofazovihperehodivmodelipottsaztrʹomakonkuruûčimivzaêmodiâminaderevikeli AT temirs dofazovihperehodivmodelipottsaztrʹomakonkuruûčimivzaêmodiâminaderevikeli |