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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2024
|
| Online Access: | http://journalarticle.ukm.my/24107/ http://journalarticle.ukm.my/24107/1/105_110%20Paper_8.pdf |
| _version_ | 1848816014154792960 |
|---|---|
| author | Mohd Ali Khameini Ahmad, Alp, Murat Mohammad Azim Mohd Azahari, Ahmad Fadillah Embong, |
| author_facet | Mohd Ali Khameini Ahmad, Alp, Murat Mohammad Azim Mohd Azahari, Ahmad Fadillah Embong, |
| author_sort | Mohd Ali Khameini Ahmad, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T00:59:08Z |
| format | Article |
| id | oai:generic.eprints.org:24107 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:59:08Z |
| publishDate | 2024 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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 |
| 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 |
| title | 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_short | 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 |
| url | http://journalarticle.ukm.my/24107/ http://journalarticle.ukm.my/24107/ http://journalarticle.ukm.my/24107/1/105_110%20Paper_8.pdf |