Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures
We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts–Bethe mapping over Qp for the prime numbers p≡...
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Springer New York LLC
2018
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| Online Access: | http://irep.iium.edu.my/65048/ http://irep.iium.edu.my/65048/2/65048_Periodic%20p-adic%20Gibbs%20Measures_SCOPUS.pdf http://irep.iium.edu.my/65048/3/65048_Periodic%20p-adic%20Gibbs%20Measures_WoS.pdf http://irep.iium.edu.my/65048/19/65048_Periodic%20p-adic%20Gibbs%20measures%20of%20q-State_MYRA.pdf |
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| author | Ahmad, Mohd Ali Khameini Liao, Lingmin Saburov, Mansoor |
| author_facet | Ahmad, Mohd Ali Khameini Liao, Lingmin Saburov, Mansoor |
| author_sort | Ahmad, Mohd Ali Khameini |
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| description | We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts–Bethe mapping over Qp for the prime numbers p≡1 (mod 3) . In fact, for 0<|θ−1|p<|q|2p<1 where θ=expp(J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0<|q|2p≤|θ−1|p<|q|p<1 , there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r≥4 . However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts–Bethe mapping are also discussed. On the other hand, for 0<|θ−1|p<|q|p<1, we remark that the Potts–Bethe mapping is not chaotic when p=3 and p≡2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0<|q|p≤|θ−1|p<1 for all prime numbers p. |
| first_indexed | 2025-11-14T17:07:10Z |
| format | Article |
| id | iium-65048 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:07:10Z |
| publishDate | 2018 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-650482018-10-02T08:26:19Z http://irep.iium.edu.my/65048/ Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures Ahmad, Mohd Ali Khameini Liao, Lingmin Saburov, Mansoor Q Science (General) We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts–Bethe mapping over Qp for the prime numbers p≡1 (mod 3) . In fact, for 0<|θ−1|p<|q|2p<1 where θ=expp(J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0<|q|2p≤|θ−1|p<|q|p<1 , there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r≥4 . However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts–Bethe mapping are also discussed. On the other hand, for 0<|θ−1|p<|q|p<1, we remark that the Potts–Bethe mapping is not chaotic when p=3 and p≡2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0<|q|p≤|θ−1|p<1 for all prime numbers p. Springer New York LLC 2018-06-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/65048/2/65048_Periodic%20p-adic%20Gibbs%20Measures_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/65048/3/65048_Periodic%20p-adic%20Gibbs%20Measures_WoS.pdf application/pdf en http://irep.iium.edu.my/65048/19/65048_Periodic%20p-adic%20Gibbs%20measures%20of%20q-State_MYRA.pdf Ahmad, Mohd Ali Khameini and Liao, Lingmin and Saburov, Mansoor (2018) Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures. Journal of Statistical Physics, 171 (6). pp. 1000-1034. ISSN 0022-4715 (In Press) https://link.springer.com/article/10.1007/s10955-018-2053-6 10.1007/s10955-018-2053-6 |
| spellingShingle | Q Science (General) Ahmad, Mohd Ali Khameini Liao, Lingmin Saburov, Mansoor Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title | Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title_full | Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title_fullStr | Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title_full_unstemmed | Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title_short | Periodic p-adic Gibbs measures of q-State potts model on Cayley Trees I: The chaos implies the vastness of the set of p-Adic Gibbs measures |
| title_sort | periodic p-adic gibbs measures of q-state potts model on cayley trees i: the chaos implies the vastness of the set of p-adic gibbs measures |
| topic | Q Science (General) |
| url | http://irep.iium.edu.my/65048/ http://irep.iium.edu.my/65048/ http://irep.iium.edu.my/65048/ http://irep.iium.edu.my/65048/2/65048_Periodic%20p-adic%20Gibbs%20Measures_SCOPUS.pdf http://irep.iium.edu.my/65048/3/65048_Periodic%20p-adic%20Gibbs%20Measures_WoS.pdf http://irep.iium.edu.my/65048/19/65048_Periodic%20p-adic%20Gibbs%20measures%20of%20q-State_MYRA.pdf |