Classification of fixed points of Potts–Bethe Mapping of degree four on Q5

Classification of fixed points of Potts–Bethe Mapping of degree four on Q5

The Potts–Bethe mapping is a rational function arises in the study of the Potts model on the Cayley tree (or Bethe lattice). In this paper, the Potts–Bethe mapping of degree four is considered over the field Q5 of 5-adic numbers. In some regimes (a condition appear in the study of p-adic Potts model...

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Main Authors: Mohd Ali Khameini Ahmad, Alp, Murat, Mohammad Azim Mohd Azahari, Ahmad Fadillah Embong
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2024
Online Access:http://journalarticle.ukm.my/24107/1/105_110%20Paper_8.pdf
http://journalarticle.ukm.my/24107/
http://www.ukm.my/jqma
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Institution: Universiti Kebangsaan Malaysia
Language: English
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spelling my-ukm.journal.241072024-09-06T00:56:21Z http://journalarticle.ukm.my/24107/ Classification of fixed points of Potts–Bethe Mapping of degree four on Q5 Mohd Ali Khameini Ahmad, Alp, Murat Mohammad Azim Mohd Azahari, Ahmad Fadillah Embong, The Potts–Bethe mapping is a rational function arises in the study of the Potts model on the Cayley tree (or Bethe lattice). In this paper, the Potts–Bethe mapping of degree four is considered over the field Q5 of 5-adic numbers. In some regimes (a condition appear in the study of p-adic Potts model), the fixed points are found and their stability are determined. It is done by solving some quartic equation over Q5 and calculating the value of derivative at each fixed points. This is the continuation of the previous work where contraction and chaos are found, but here other property is realized such as 1-Lipschitz. Penerbit Universiti Kebangsaan Malaysia 2024-07 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/24107/1/105_110%20Paper_8.pdf Mohd Ali Khameini Ahmad, and Alp, Murat and Mohammad Azim Mohd Azahari, and Ahmad Fadillah Embong, (2024) Classification of fixed points of Potts–Bethe Mapping of degree four on Q5. Journal of Quality Measurement and Analysis, 20 (2). pp. 105-110. ISSN 2600-8602 http://www.ukm.my/jqma
institution Universiti Kebangsaan Malaysia
building Tun Sri Lanang Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Kebangsaan Malaysia
content_source UKM Journal Article Repository
url_provider http://journalarticle.ukm.my/
language English
description The Potts–Bethe mapping is a rational function arises in the study of the Potts model on the Cayley tree (or Bethe lattice). In this paper, the Potts–Bethe mapping of degree four is considered over the field Q5 of 5-adic numbers. In some regimes (a condition appear in the study of p-adic Potts model), the fixed points are found and their stability are determined. It is done by solving some quartic equation over Q5 and calculating the value of derivative at each fixed points. This is the continuation of the previous work where contraction and chaos are found, but here other property is realized such as 1-Lipschitz.
format Article
author Mohd Ali Khameini Ahmad,
Alp, Murat
Mohammad Azim Mohd Azahari,
Ahmad Fadillah Embong,
spellingShingle Mohd Ali Khameini Ahmad,
Alp, Murat
Mohammad Azim Mohd Azahari,
Ahmad Fadillah Embong,
Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
author_facet Mohd Ali Khameini Ahmad,
Alp, Murat
Mohammad Azim Mohd Azahari,
Ahmad Fadillah Embong,
author_sort Mohd Ali Khameini Ahmad,
title Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
title_short Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
title_full Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
title_fullStr Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
title_full_unstemmed Classification of fixed points of Potts–Bethe Mapping of degree four on Q5
title_sort classification of fixed points of potts–bethe mapping of degree four on q5
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2024
url http://journalarticle.ukm.my/24107/1/105_110%20Paper_8.pdf
http://journalarticle.ukm.my/24107/
http://www.ukm.my/jqma
_version_ 1811683406043414528

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