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

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	4430/43608
Uncontrolled Keywords:	q-state Potts model, Cayley tree, Modulated phase, Paramodulated phase
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	14 Jul 2015 11:13
Last Modified:	17 Nov 2017 14:27
URI:	http://irep.iium.edu.my/id/eprint/43608

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