On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees
In this paper, the lambda-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if lambda-function is taken as a Potts interaction function, then this model reduces to the Potts model with competing interactions. The Pot...
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Elsevier
2020
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iium-784042020-03-04T02:39:13Z http://irep.iium.edu.my/78404/ On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahmatullaev, Muzaffar QA Mathematics In this paper, the lambda-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if lambda-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 2020 Article PeerReviewed application/pdf en http://irep.iium.edu.my/78404/7/78404%20On%20ground%20states%20and%20phase%20transition-in-press.pdf application/pdf en http://irep.iium.edu.my/78404/8/78404%20On%20ground%20states%20and%20phase%20transition-in-press-SCOPUS.pdf Mukhamedov, Farrukh and Pah, Chin Hee and Jamil, Hakim and Rahmatullaev, 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. ISSN 03784371 (In Press) https://www.sciencedirect.com/science/article/pii/S0378437120300273 10.1016/j.physa.2020.124184 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
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IIUM Repository |
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Online Access |
| language |
English English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahmatullaev, Muzaffar On ground states and phase transition for λ-model with the competing Potts interactions on Cayley trees |
| description |
In this paper, the lambda-model with nearest neighbor interactions is considered with competing Potts interactions on the Cayley tree of order-two. Notice that if lambda-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. |
| format |
Article |
| author |
Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahmatullaev, Muzaffar |
| author_facet |
Mukhamedov, Farrukh Pah, Chin Hee Jamil, Hakim Rahmatullaev, Muzaffar |
| author_sort |
Mukhamedov, Farrukh |
| title |
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_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_sort |
on ground states and phase transition for λ-model with the competing potts interactions on cayley trees |
| publisher |
Elsevier |
| publishDate |
2020 |
| url |
http://irep.iium.edu.my/78404/ http://irep.iium.edu.my/78404/ http://irep.iium.edu.my/78404/ http://irep.iium.edu.my/78404/7/78404%20On%20ground%20states%20and%20phase%20transition-in-press.pdf http://irep.iium.edu.my/78404/8/78404%20On%20ground%20states%20and%20phase%20transition-in-press-SCOPUS.pdf |
| first_indexed |
2023-09-18T21:50:29Z |
| last_indexed |
2023-09-18T21:50:29Z |
| _version_ |
1777413736091353088 |