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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/140557 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-140557 |
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dspace |
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irk-123456789-1405572018-07-11T01:23:14Z On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree Rahmatullaev, M.M. 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. 2016 Article 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) http://dspace.nbuv.gov.ua/handle/123456789/140557 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Rahmatullaev, M.M. |
| spellingShingle |
Rahmatullaev, M.M. On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree Журнал математической физики, анализа, геометрии |
| author_facet |
Rahmatullaev, M.M. |
| author_sort |
Rahmatullaev, M.M. |
| title |
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_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_sort |
on weakly periodic gibbs measures of the potts model with a special external field on a cayley tree |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140557 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
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2023-10-18T21:22:55Z |
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