On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree
In the paper, we study the q-state (where q = 3, 4, 5, ... ) Potts model with special external field on a Cayley tree of order k ≥ 2. For antiferromagnetic Potts model with such an external field on the Cayley tree of order k ≥ 6, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures i...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140557 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree / M.M. Rahmatullaev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 302-314. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862593761855406080 |
|---|---|
| author | Rahmatullaev, M.M. |
| author_facet | Rahmatullaev, M.M. |
| citation_txt | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree / M.M. Rahmatullaev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 302-314. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | In the paper, we study the q-state (where q = 3, 4, 5, ... ) Potts model with special external field on a Cayley tree of order k ≥ 2. For antiferromagnetic Potts model with such an external field on the Cayley tree of order k ≥ 6, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures is proved. The weakly periodic Gibbs measures for the Potts model with zero external field are also studied. It is proved that under some conditions imposed on the parameters of the model there can be not less than 2q - 2 such measures.
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| first_indexed | 2025-11-27T10:31:11Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-140557 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-27T10:31:11Z |
| publishDate | 2016 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Rahmatullaev, M.M. 2018-07-10T16:10:26Z 2018-07-10T16:10:26Z 2016 On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree / M.M. Rahmatullaev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 302-314. — Бібліогр.: 16 назв. — англ. 1812-9471 DOI : doi.org/10.15407/mag12.04.302 Mathematics Subject Classification 2000: 82B26 (primary); 60K35 (secondary) https://nasplib.isofts.kiev.ua/handle/123456789/140557 In the paper, we study the q-state (where q = 3, 4, 5, ... ) Potts model with special external field on a Cayley tree of order k ≥ 2. For antiferromagnetic Potts model with such an external field on the Cayley tree of order k ≥ 6, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures is proved. The weakly periodic Gibbs measures for the Potts model with zero external field are also studied. It is proved that under some conditions imposed on the parameters of the model there can be not less than 2q - 2 such measures. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree Article published earlier |
| spellingShingle | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree Rahmatullaev, M.M. |
| title | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree |
| title_full | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree |
| title_fullStr | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree |
| title_full_unstemmed | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree |
| title_short | On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree |
| title_sort | on weakly periodic gibbs measures of the potts model with a special external field on a cayley tree |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140557 |
| work_keys_str_mv | AT rahmatullaevmm onweaklyperiodicgibbsmeasuresofthepottsmodelwithaspecialexternalfieldonacayleytree |