On Ising model with four competing interactions on Cayley tree
In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. Our second result gives complete de...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2009
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| Online Access: | http://irep.iium.edu.my/1642/ http://irep.iium.edu.my/1642/1/Ising_with_4_inter.pdf |
| _version_ | 1848775890620645376 |
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| author | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_facet | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. Our second result gives
complete description of the periodic Gibbs measures for the model. We also construct uncountably many non-periodic extreme Gibbs measures. |
| first_indexed | 2025-11-14T14:21:23Z |
| format | Article |
| id | iium-1642 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:23Z |
| publishDate | 2009 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16422011-11-22T00:46:42Z http://irep.iium.edu.my/1642/ On Ising model with four competing interactions on Cayley tree Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics In the paper we consider an Ising model with four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) on the Cayley tree of order two.We show that for some parameter values of the model there is a phase transition. Our second result gives complete description of the periodic Gibbs measures for the model. We also construct uncountably many non-periodic extreme Gibbs measures. Springer Netherlands 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1642/1/Ising_with_4_inter.pdf Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2009) On Ising model with four competing interactions on Cayley tree. Mathematical Physics, Analysis and Geometry, 12 (2). pp. 141-156. ISSN 1385-0172 (P), 1572-9656 (O) http://www.springerlink.com/content/47m312707366001p/ 10.1007/s11040-009-9056-0 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich On Ising model with four competing interactions on Cayley tree |
| title | On Ising model with four competing interactions on Cayley tree |
| title_full | On Ising model with four competing interactions on Cayley tree |
| title_fullStr | On Ising model with four competing interactions on Cayley tree |
| title_full_unstemmed | On Ising model with four competing interactions on Cayley tree |
| title_short | On Ising model with four competing interactions on Cayley tree |
| title_sort | on ising model with four competing interactions on cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1642/ http://irep.iium.edu.my/1642/ http://irep.iium.edu.my/1642/ http://irep.iium.edu.my/1642/1/Ising_with_4_inter.pdf |