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...

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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/ http://irep.iium.edu.my/43608/ http://irep.iium.edu.my/43608/ 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

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spelling	iium-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 PeerReviewed 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
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
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/ http://irep.iium.edu.my/43608/ http://irep.iium.edu.my/43608/ 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
first_indexed	2023-09-18T21:02:08Z
last_indexed	2023-09-18T21:02:08Z
_version_	1777410693814812672

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

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