On the strong phase transition for the one-dimensional countable statep-adic Potts model
In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the pr...
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing Ltd.
2014
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| Online Access: | http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf |
| _version_ | 1825647905563738112 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| description | In the present paper we consider the countable state p-adic Potts
model on Z+. A main aim is to establish the existence of the strong phase
transition for the model. In our study, we essentially use one dimensionality
of the model. To prove the existence of the phase transition, we reduce the
problem to the investigation of an in�nite-dimensional nonlinear equation. We
�nd a condition on weights to show that the derived equation has two solutions.
We show that measures corresponding to �rst and second solutions are a p-adic
Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved
that the p-adic Gibbs measure is bounded, and the generalized one is not
bounded. This implies the existence of the strong phase transition. Note that
it turns out that the obtained condition does not depend on values of the prime
p and, therefore, an analogous fact is not true when the number of spins is �nite.
Note that, in the usual real case, if one considers a one-dimensional translation-
invariant model with nearest neighbor interaction, then such a model does not
exhibit a phase transition. Nevertheless, we should stress that our model exhibits
a unique p-adic Gibbs measure. |
| first_indexed | 2024-03-05T23:24:28Z |
| format | Article |
| id | oai:generic.eprints.org:35681 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:24:28Z |
| publishDate | 2014 |
| publisher | Institute of Physics Publishing Ltd. |
| record_format | dspace |
| spelling | oai:generic.eprints.org:356812014-02-19T03:12:08Z http://irep.iium.edu.my/35681/ On the strong phase transition for the one-dimensional countable statep-adic Potts model Mukhamedov, Farrukh QA Mathematics QC Physics In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the problem to the investigation of an in�nite-dimensional nonlinear equation. We �nd a condition on weights to show that the derived equation has two solutions. We show that measures corresponding to �rst and second solutions are a p-adic Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved that the p-adic Gibbs measure is bounded, and the generalized one is not bounded. This implies the existence of the strong phase transition. Note that it turns out that the obtained condition does not depend on values of the prime p and, therefore, an analogous fact is not true when the number of spins is �nite. Note that, in the usual real case, if one considers a one-dimensional translation- invariant model with nearest neighbor interaction, then such a model does not exhibit a phase transition. Nevertheless, we should stress that our model exhibits a unique p-adic Gibbs measure. Institute of Physics Publishing Ltd. 2014 Article PeerReviewed application/pdf en http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf Mukhamedov, Farrukh (2014) On the strong phase transition for the one-dimensional countable statep-adic Potts model. Journal of Statistical Mechanics: Theory and Experiment, 2014 (P01007). pp. 1-23. ISSN 1742-5468 (O) http://dx.doi.org/10.1088/1742-5468/2014/01/P01007 doi:10.1088/1742-5468/2014/01/P01007 |
| spellingShingle | QA Mathematics QC Physics Mukhamedov, Farrukh On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title | On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title_full | On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title_fullStr | On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title_full_unstemmed | On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title_short | On the strong phase transition for the one-dimensional countable statep-adic Potts model |
| title_sort | on the strong phase transition for the one dimensional countable statep adic potts model |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf |
| work_keys_str_mv | AT mukhamedovfarrukh onthestrongphasetransitionfortheonedimensionalcountablestatepadicpottsmodel |