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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/49321/1/saburov2015.pdf http://irep.iium.edu.my/49321/ http://link.springer.com/article/10.1007/s11040-015-9194-5 |
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| Institution: | Universiti Islam Antarabangsa Malaysia |
| Language: | English |
| Summary: | 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. |
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