Existence of phase transition for 1d-countable state P -adic Potts model
In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation o...
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| Format: | Book Chapter |
| Language: | English |
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ASR MATBUOT” ltd.
2012
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| Online Access: | http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf |
| _version_ | 1825646831431843840 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| description | In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation of an infinitedimensional nonlinear equation. We find a condition on weights to show that the
derived equation has two solutions, which yields the existence of the phase transition. We prove that measures corresponding to first and second solutions are a p -adic Gibbs and generalized p -adic Gibbs measures, respectively. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite |
| first_indexed | 2024-03-05T23:08:28Z |
| format | Book Chapter |
| id | oai:generic.eprints.org:26068 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-13T18:59:14Z |
| publishDate | 2012 |
| publisher | ASR MATBUOT” ltd. |
| record_format | dspace |
| spelling | oai:generic.eprints.org:260682012-12-31T03:40:56Z http://irep.iium.edu.my/26068/ Existence of phase transition for 1d-countable state P -adic Potts model Mukhamedov, Farrukh QA Mathematics In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation of an infinitedimensional nonlinear equation. We find a condition on weights to show that the derived equation has two solutions, which yields the existence of the phase transition. We prove that measures corresponding to first and second solutions are a p -adic Gibbs and generalized p -adic Gibbs measures, respectively. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite ASR MATBUOT” ltd. 2012 Book Chapter PeerReviewed application/pdf en http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf Mukhamedov, Farrukh (2012) Existence of phase transition for 1d-countable state P -adic Potts model. In: Proceedings of Turin Polytechnic University in Tashkent. ASR MATBUOT” ltd., Tashkent, Uzbekistan, pp. 228-242. |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Existence of phase transition for 1d-countable state P -adic Potts model |
| title | Existence of phase transition for 1d-countable state P -adic
Potts model |
| title_full | Existence of phase transition for 1d-countable state P -adic
Potts model |
| title_fullStr | Existence of phase transition for 1d-countable state P -adic
Potts model |
| title_full_unstemmed | Existence of phase transition for 1d-countable state P -adic
Potts model |
| title_short | Existence of phase transition for 1d-countable state P -adic
Potts model |
| title_sort | existence of phase transition for 1d countable state p adic potts model |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf |
| work_keys_str_mv | AT mukhamedovfarrukh existenceofphasetransitionfor1dcountablestatepadicpottsmodel |