On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three
Unlike the real number field, a set of p−adic Gibbs measures of p−adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p−adic fields. Recently, all translation-invariant p−adic Gibbs measures of the p−adic Potts...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2015
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| Online Access: | http://irep.iium.edu.my/49321/1/saburov2015.pdf |
| _version_ | 1825649517458882560 |
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| author | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_facet | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_sort | Saburov, Mansoor |
| collection | IIUM |
| description | Unlike the real number field, a set of p−adic Gibbs measures of p−adic lattice models of statistical mechanics has a complex structure in a sense that it
is strongly tied up with a Diophantine problem over p−adic fields. Recently, all translation-invariant p−adic Gibbs measures of the p−adic Potts model on the Cayley
tree of order two were described by means of roots of a certain quadratic equation over some domain of the p−adic field. In this paper, we consider the same problem
on the Cayley tree of order three. In this case, we show that all translation-invariant p−adic Gibbs measures of the p−adic Potts model can be described in terms of roots
of some cubic equation over Zp \ Z∗p. In own its turn, we also provide a solvability criterion of a general cubic equation over Zp \ Z∗p for p > 3. |
| first_indexed | 2024-03-05T23:48:43Z |
| format | Article |
| id | oai:generic.eprints.org:49321 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:48:43Z |
| publishDate | 2015 |
| publisher | Springer |
| record_format | dspace |
| spelling | oai:generic.eprints.org:493212016-02-23T09:14:30Z http://irep.iium.edu.my/49321/ On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three Saburov, Mansoor Ahmad, Mohd Ali Khameini QA Mathematics Unlike the real number field, a set of p−adic Gibbs measures of p−adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p−adic fields. Recently, all translation-invariant p−adic Gibbs measures of the p−adic Potts model on the Cayley tree of order two were described by means of roots of a certain quadratic equation over some domain of the p−adic field. In this paper, we consider the same problem on the Cayley tree of order three. In this case, we show that all translation-invariant p−adic Gibbs measures of the p−adic Potts model can be described in terms of roots of some cubic equation over Zp \ Z∗p. In own its turn, we also provide a solvability criterion of a general cubic equation over Zp \ Z∗p for p > 3. Springer 2015-09-23 Article PeerReviewed application/pdf en http://irep.iium.edu.my/49321/1/saburov2015.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2015) On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three. Mathematical Physics, Analysis and Geometry, 18 (1). pp. 1-33. ISSN 1385-0172 http://link.springer.com/article/10.1007/s11040-015-9194-5 10.1007/s11040-015-9194-5 |
| spellingShingle | QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title | On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title_full | On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title_fullStr | On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title_full_unstemmed | On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title_short | On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| title_sort | on descriptions of all translation invariant p adic gibbs measures for the potts model on the cayley tree of order three |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/49321/1/saburov2015.pdf |
| work_keys_str_mv | AT saburovmansoor ondescriptionsofalltranslationinvariantpadicgibbsmeasuresforthepottsmodelonthecayleytreeoforderthree AT ahmadmohdalikhameini ondescriptionsofalltranslationinvariantpadicgibbsmeasuresforthepottsmodelonthecayleytreeoforderthree |