Cover Image

The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree

In this paper, we study the phase diagrams for the integer q-state (q ≥ 3) Potts model on a Cayley tree for order two with competing nearest-neighbor interactions J 1, prolonged next-nearestneighbor interactions J p and two-level triple-neighbor interactions J t . The exact phase diagrams of the Pot...

Full description

Saved in:
Bibliographic Details
Main Authors: Uguz, Selman, Ganikhodjaev, Nasir, Dogan, Hasan
Format: Article
Language:English
English
Published: The Korean Physical Society 2015
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/43608/1/J_Korean_Phys_2015_Selman.pdf
http://irep.iium.edu.my/43608/4/43608_The%20Hamiltonian%20three-parameter%20spaces%20of%20the%20q%20-state%20Potts%20model_SCOPUS.pdf
http://irep.iium.edu.my/43608/
http://link.springer.com/article/10.3938%2Fjkps.66.1467
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.iium.irep.43608
record_format dspace
spelling my.iium.irep.436082017-11-17T06:27:29Z http://irep.iium.edu.my/43608/ The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree Uguz, Selman Ganikhodjaev, Nasir Dogan, Hasan QA Mathematics In this paper, we study the phase diagrams for the integer q-state (q ≥ 3) Potts model on a Cayley tree for order two with competing nearest-neighbor interactions J 1, prolonged next-nearestneighbor interactions J p and two-level triple-neighbor interactions J t . The exact phase diagrams of the Potts model with some competing interactions on a Cayley tree lattice of order two have been found. At vanishing temperature, the phase diagram is fully determined for all values and signs of J 1, J p and J t . Our aim is to generalize the results of Ganikhodjaev et al. to the q-state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level tripleneighbor interactions on a Cayley tree for order 2 and to compare these with previous results in the literature. Ganikhodjaev et al. reported on a new phase, denoted as a paramodulated (PM) phase, found at low temperatures and characterized by 2-periodic points of an one-dimensional dynamical system lying inside the modulated phase. An important note for such a phase is that inherently the Potts model has no analogues in the Ising setting. In this paper, we show that increasing the spin number from three (q = 3) to arbitrary q > 3 can dramatically affect the resultant phases (expanding the paramodulated phase). We believe that the enlarging of the paramodulated (PM) phase is essentially connected to the symmetry in the spin numbers. The Korean Physical Society 2015-05 Article REM application/pdf en http://irep.iium.edu.my/43608/1/J_Korean_Phys_2015_Selman.pdf application/pdf en http://irep.iium.edu.my/43608/4/43608_The%20Hamiltonian%20three-parameter%20spaces%20of%20the%20q%20-state%20Potts%20model_SCOPUS.pdf Uguz, Selman and Ganikhodjaev, Nasir and Dogan, Hasan (2015) The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree. Journal of the Korean Physical Society, 66 (10). pp. 1467-1474. ISSN 0374-4884 (P) 1976-8524 (O) http://link.springer.com/article/10.3938%2Fjkps.66.1467 10.3938/jkps.66.1467
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Uguz, Selman
Ganikhodjaev, Nasir
Dogan, Hasan
The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
description In this paper, we study the phase diagrams for the integer q-state (q ≥ 3) Potts model on a Cayley tree for order two with competing nearest-neighbor interactions J 1, prolonged next-nearestneighbor interactions J p and two-level triple-neighbor interactions J t . The exact phase diagrams of the Potts model with some competing interactions on a Cayley tree lattice of order two have been found. At vanishing temperature, the phase diagram is fully determined for all values and signs of J 1, J p and J t . Our aim is to generalize the results of Ganikhodjaev et al. to the q-state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level tripleneighbor interactions on a Cayley tree for order 2 and to compare these with previous results in the literature. Ganikhodjaev et al. reported on a new phase, denoted as a paramodulated (PM) phase, found at low temperatures and characterized by 2-periodic points of an one-dimensional dynamical system lying inside the modulated phase. An important note for such a phase is that inherently the Potts model has no analogues in the Ising setting. In this paper, we show that increasing the spin number from three (q = 3) to arbitrary q > 3 can dramatically affect the resultant phases (expanding the paramodulated phase). We believe that the enlarging of the paramodulated (PM) phase is essentially connected to the symmetry in the spin numbers.
format Article
author Uguz, Selman
Ganikhodjaev, Nasir
Dogan, Hasan
author_facet Uguz, Selman
Ganikhodjaev, Nasir
Dogan, Hasan
author_sort Uguz, Selman
title The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
title_short The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
title_full The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
title_fullStr The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
title_full_unstemmed The Hamiltonian three-parameter spaces of the q -state Potts model with three competing interactions on a Cayley tree
title_sort hamiltonian three-parameter spaces of the q -state potts model with three competing interactions on a cayley tree
publisher The Korean Physical Society
publishDate 2015
url http://irep.iium.edu.my/43608/1/J_Korean_Phys_2015_Selman.pdf
http://irep.iium.edu.my/43608/4/43608_The%20Hamiltonian%20three-parameter%20spaces%20of%20the%20q%20-state%20Potts%20model_SCOPUS.pdf
http://irep.iium.edu.my/43608/
http://link.springer.com/article/10.3938%2Fjkps.66.1467
_version_ 1643612422859128832
score 13.211869

Similar Items