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≡...

Full description

Bibliographic Details
Main Authors:	Ahmad, Mohd Ali Khameini, Liao, Lingmin, Saburov, Mansoor
Format:	Article
Language:	English English English
Published:	Springer New York LLC 2018
Subjects:	Q Science (General)
Online Access:	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

id	iium-65048
recordtype	eprints
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
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	Q Science (General)
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
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.
format	Article
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
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_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_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_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
publisher	Springer New York LLC
publishDate	2018
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
first_indexed	2023-09-18T21:32:17Z
last_indexed	2023-09-18T21:32:17Z
_version_	1777412591147024384

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

Similar Items