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


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2015-05

AUTHORS

Selman Uguz, Nasir Ganikhodjaev, Hasan Dogan

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 J1, prolonged next-nearestneighbor interactions Jp and two-level triple-neighbor interactions Jt. 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 J1, Jp and Jt. 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. More... »

PAGES

1467-1474

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.3938/jkps.66.1467

DOI

http://dx.doi.org/10.3938/jkps.66.1467

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1012352244


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