On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees
In this paper, the λ-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if λ-function is taken as a Potts interaction function, then this model reduces to the Potts model with competing interactions. The Potts model w...
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| Format: | Article |
| Language: | English English English |
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Elsevier B.V.
2020
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| Online Access: | http://irep.iium.edu.my/80398/ http://irep.iium.edu.my/80398/1/80398_On%20ground%20states%20and%20phase%20transition.pdf http://irep.iium.edu.my/80398/2/80398_On%20ground%20states%20and%20phase%20transition_SCOPUS.pdf http://irep.iium.edu.my/80398/3/80398_On%20ground%20states%20and%20phase%20transition_WOS.pdf |
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| author | Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahimatullaev, Muzaffar |
| author_facet | Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahimatullaev, Muzaffar |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper, the λ-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if λ-function is taken as a Potts interaction function, then this model reduces to the Potts model with competing interactions. The Potts model with considered interactions has only been numerically investigated, hence we aim to propose a measure-theoretical approach for the considered model in a more general setting. Therefore, first ground states of the model are described. Furthermore, certain conditions for the existence of Gibbs measures corresponding to the model are found, which allows the establishment of the existence of the phase transition. |
| first_indexed | 2025-11-14T17:48:59Z |
| format | Article |
| id | iium-80398 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:48:59Z |
| publishDate | 2020 |
| publisher | Elsevier B.V. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-803982020-05-08T16:10:02Z http://irep.iium.edu.my/80398/ On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahimatullaev, Muzaffar Q Science (General) In this paper, the λ-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if λ-function is taken as a Potts interaction function, then this model reduces to the Potts model with competing interactions. The Potts model with considered interactions has only been numerically investigated, hence we aim to propose a measure-theoretical approach for the considered model in a more general setting. Therefore, first ground states of the model are described. Furthermore, certain conditions for the existence of Gibbs measures corresponding to the model are found, which allows the establishment of the existence of the phase transition. Elsevier B.V. 2020-06-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/80398/1/80398_On%20ground%20states%20and%20phase%20transition.pdf application/pdf en http://irep.iium.edu.my/80398/2/80398_On%20ground%20states%20and%20phase%20transition_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/80398/3/80398_On%20ground%20states%20and%20phase%20transition_WOS.pdf Mukhamedov, Farrukh and Pah, Chin Hee and Jamil, Hakim and Rahimatullaev, Muzaffar (2020) On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees. Physica A: Statistical Mechanics and its Applications, 549. pp. 1-18. ISSN 0378-4371 E-ISSN 1873-2119 https://www.sciencedirect.com/science/article/pii/S0378437120300273 10.1016/j.physa.2020.124184 |
| spellingShingle | Q Science (General) Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahimatullaev, Muzaffar On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title | On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title_full | On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title_fullStr | On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title_full_unstemmed | On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title_short | On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| title_sort | on ground states and phase transition for λ-model with the competing potts interactions on cayley trees |
| topic | Q Science (General) |
| url | http://irep.iium.edu.my/80398/ http://irep.iium.edu.my/80398/ http://irep.iium.edu.my/80398/ http://irep.iium.edu.my/80398/1/80398_On%20ground%20states%20and%20phase%20transition.pdf http://irep.iium.edu.my/80398/2/80398_On%20ground%20states%20and%20phase%20transition_SCOPUS.pdf http://irep.iium.edu.my/80398/3/80398_On%20ground%20states%20and%20phase%20transition_WOS.pdf |