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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Elsevier
2007
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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 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Ganikhodjaev, Nasir Limiting Gibbs measures of Potts model with countable set of spin values |
| 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. |
| format |
Article |
| author |
Ganikhodjaev, Nasir |
| author_facet |
Ganikhodjaev, Nasir |
| author_sort |
Ganikhodjaev, Nasir |
| title |
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_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_sort |
limiting gibbs measures of potts model with countable set of spin values |
| publisher |
Elsevier |
| publishDate |
2007 |
| 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 |
| first_indexed |
2023-09-18T20:09:04Z |
| last_indexed |
2023-09-18T20:09:04Z |
| _version_ |
1777407355332329472 |