The Potts model with countable set of spin values on a Cayley tree
We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite sys...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2006
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| Online Access: | http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf |
| _version_ | 1848777692427583488 |
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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 | We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study
translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k�1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0, 1, . . . } we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give description of the class of measures ν on Φ such that with respect to each element of this class our infinite system of equations has unique solution
{ai , i =1, 2, . . . }, where a ∈(0, 1). |
| first_indexed | 2025-11-14T14:50:01Z |
| format | Article |
| id | iium-14417 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:50:01Z |
| publishDate | 2006 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-144172012-05-31T02:33:27Z http://irep.iium.edu.my/14417/ The Potts model with countable set of spin values on a Cayley tree Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k�1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0, 1, . . . } we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give description of the class of measures ν on Φ such that with respect to each element of this class our infinite system of equations has unique solution {ai , i =1, 2, . . . }, where a ∈(0, 1). Springer Netherlands 2006 Article PeerReviewed application/pdf en http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2006) The Potts model with countable set of spin values on a Cayley tree. Letters in Mathematical Physics, 75 (2). pp. 99-109. ISSN 0377-9017 (P), 1573-0530 (O) http://www.springerlink.com/content/yp736185774p5304/ 10.1007/s11005-005-0032-8 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich The Potts model with countable set of spin values on a Cayley tree |
| title | The Potts model with countable set of spin values on a Cayley tree
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| title_full | The Potts model with countable set of spin values on a Cayley tree
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| title_fullStr | The Potts model with countable set of spin values on a Cayley tree
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| title_full_unstemmed | The Potts model with countable set of spin values on a Cayley tree
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| title_short | The Potts model with countable set of spin values on a Cayley tree
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| title_sort | potts model with countable set of spin values on a cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf |