Limiting Gibbs measures of Potts model with countable set of spin values
We consider a nearest-neighbor Potts model, with countable spin values Φ = {0, 1, . . .}, and nonzero external field, on a Cayley tree of order k (with k + 1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. The problem is reduced to the description of the solutions of some infi...
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| Format: | Article |
| Language: | English |
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Elsevier
2007
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| Online Access: | http://irep.iium.edu.my/1645/ http://irep.iium.edu.my/1645/1/JMAA_paper.pdf |
| _version_ | 1848775891583238144 |
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| author | Ganikhodjaev, Nasir |
| author_facet | Ganikhodjaev, Nasir |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | We consider a nearest-neighbor Potts model, with countable spin values Φ = {0, 1, . . .}, and nonzero external field, on a Cayley tree of order k (with k + 1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. The problem is reduced to the description of the solutions of some infinite system of equations. We give full description of the class of probabilistic measures ν on Φ such that our infinite system of equations has unique solution with respect to each element of this class. In particular we describe the Poisson measures which are Gibbsian. |
| first_indexed | 2025-11-14T14:21:24Z |
| format | Article |
| id | iium-1645 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:24Z |
| publishDate | 2007 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16452011-11-21T14:20:59Z http://irep.iium.edu.my/1645/ Limiting Gibbs measures of Potts model with countable set of spin values Ganikhodjaev, Nasir QA Mathematics We consider a nearest-neighbor Potts model, with countable spin values Φ = {0, 1, . . .}, and nonzero external field, on a Cayley tree of order k (with k + 1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. The problem is reduced to the description of the solutions of some infinite system of equations. We give full description of the class of probabilistic measures ν on Φ such that our infinite system of equations has unique solution with respect to each element of this class. In particular we describe the Poisson measures which are Gibbsian. Elsevier 2007-03-13 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1645/1/JMAA_paper.pdf Ganikhodjaev, Nasir (2007) Limiting Gibbs measures of Potts model with countable set of spin values. Journal of Mathematical Analysis and Applications, 336 (1). pp. 693-703. ISSN 0022-247X http://www.sciencedirect.com/science/article/pii/S0022247X07003150 10.1016/j.jmaa.2007.03.013 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Limiting Gibbs measures of Potts model with countable set of spin values |
| title | Limiting Gibbs measures of Potts model with countable set of spin values |
| title_full | Limiting Gibbs measures of Potts model with countable set of spin values |
| title_fullStr | Limiting Gibbs measures of Potts model with countable set of spin values |
| title_full_unstemmed | Limiting Gibbs measures of Potts model with countable set of spin values |
| title_short | Limiting Gibbs measures of Potts model with countable set of spin values |
| title_sort | limiting gibbs measures of potts model with countable set of spin values |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1645/ http://irep.iium.edu.my/1645/ http://irep.iium.edu.my/1645/ http://irep.iium.edu.my/1645/1/JMAA_paper.pdf |