Phase transition and chaos: P-adic Potts model on a Cayley tree
In our previous investigations, we have developed the renormalization group method to p -adic models on Cayley trees, this method is closely related to the investigation of dynamical system associated with a given model. In this paper, we are interested in the following question: how is the existe...
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Elsevier, Inc.
2016
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iium-503922016-12-22T06:43:58Z http://irep.iium.edu.my/50392/ Phase transition and chaos: P-adic Potts model on a Cayley tree Mukhamedov, Farrukh Khakimov, Otabek QA Mathematics In our previous investigations, we have developed the renormalization group method to p -adic models on Cayley trees, this method is closely related to the investigation of dynamical system associated with a given model. In this paper, we are interested in the following question: how is the existence of the phase transition related to chaotic behavior of the associated dynamical system (this is one of the important question in physics)? To realize this question, we consider as a toy model the p -adic q -state Potts model on a Cayley tree, and show, in the phase transition regime, the associated dynamical system is chaotic, i.e. it is conjugate to the full shift. As an application of this result, we are able to show the existence of periodic (with any period) p -adic quasi Gibbs measures for the model. This allows us to know that how large is the class of p -adic quasi Gibbs measures. We point out that a similar kind of result is not known in the case of real numbers. Elsevier, Inc. 2016-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/50392/1/mfko-CSF%282016%29.pdf application/pdf en http://irep.iium.edu.my/50392/4/50392-Phase_transition_and_chaos_SCOPUS.pdf Mukhamedov, Farrukh and Khakimov, Otabek (2016) Phase transition and chaos: P-adic Potts model on a Cayley tree. Chaos, Solitons and Fractals, 87. pp. 190-196. ISSN 0960-0779 http://www.sciencedirect.com/science/article/pii/S096007791630128X 10.1016/j.chaos.2016.04.003 |
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Digital Repository |
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Local University |
| institution |
International Islamic University Malaysia |
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IIUM Repository |
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Online Access |
| language |
English English |
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QA Mathematics |
| spellingShingle |
QA Mathematics Mukhamedov, Farrukh Khakimov, Otabek Phase transition and chaos: P-adic Potts model on a Cayley tree |
| description |
In our previous investigations, we have developed the renormalization group method to p -adic models
on Cayley trees, this method is closely related to the investigation of dynamical system associated with a
given model. In this paper, we are interested in the following question: how is the existence of the phase
transition related to chaotic behavior of the associated dynamical system (this is one of the important
question in physics)? To realize this question, we consider as a toy model the p -adic q -state Potts model
on a Cayley tree, and show, in the phase transition regime, the associated dynamical system is chaotic,
i.e. it is conjugate to the full shift. As an application of this result, we are able to show the existence of
periodic (with any period) p -adic quasi Gibbs measures for the model. This allows us to know that how
large is the class of p -adic quasi Gibbs measures. We point out that a similar kind of result is not known
in the case of real numbers. |
| format |
Article |
| author |
Mukhamedov, Farrukh Khakimov, Otabek |
| author_facet |
Mukhamedov, Farrukh Khakimov, Otabek |
| author_sort |
Mukhamedov, Farrukh |
| title |
Phase transition and chaos: P-adic Potts model on a Cayley tree |
| title_short |
Phase transition and chaos: P-adic Potts model on a Cayley tree |
| title_full |
Phase transition and chaos: P-adic Potts model on a Cayley tree |
| title_fullStr |
Phase transition and chaos: P-adic Potts model on a Cayley tree |
| title_full_unstemmed |
Phase transition and chaos: P-adic Potts model on a Cayley tree |
| title_sort |
phase transition and chaos: p-adic potts model on a cayley tree |
| publisher |
Elsevier, Inc. |
| publishDate |
2016 |
| url |
http://irep.iium.edu.my/50392/ http://irep.iium.edu.my/50392/ http://irep.iium.edu.my/50392/ http://irep.iium.edu.my/50392/1/mfko-CSF%282016%29.pdf http://irep.iium.edu.my/50392/4/50392-Phase_transition_and_chaos_SCOPUS.pdf |
| first_indexed |
2023-09-18T21:11:14Z |
| last_indexed |
2023-09-18T21:11:14Z |
| _version_ |
1777411266047901696 |