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: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer
2015
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/1/saburov2015.pdf |
| id |
iium-49321 |
|---|---|
| recordtype |
eprints |
| spelling |
iium-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 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| 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 |
| 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. |
| format |
Article |
| author |
Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_facet |
Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_sort |
Saburov, Mansoor |
| title |
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_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_sort |
on descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three |
| publisher |
Springer |
| publishDate |
2015 |
| url |
http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/ http://irep.iium.edu.my/49321/1/saburov2015.pdf |
| first_indexed |
2023-09-18T21:09:46Z |
| last_indexed |
2023-09-18T21:09:46Z |
| _version_ |
1777411173689327616 |