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- 검색키워드
- 주제어 : Cayley tree (검색결과 4 건)
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Nasir Ganikhodjaev,Mohd Hirzie Mohd Rodzhan 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.66 No.8
We study the phase diagram of the Ising model on the Cayley tree with competing interactions up to the third nearest-neighbors with spins belonging to different branches of the tree. In addition to the expected ferromagnetic, anti-ferromagnetic and paramagnetic phases, we present a new paramodulated phase. Moreover, the transition lines are analyzed and they are in agreement with the lines obtained numerically. Lastly, the stability of the anti-ferromagnetic phase was studied in detail by investigating the Lyapunov exponent associated with the corresponding dynamical system.
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Selman Uguz,Nasir Ganikhodjaev,Hasan Dogan 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.66 No.10
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.
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Potts Model with Next-nearest-neighbor Ternary Interactions on an Arbitrary-order Cayley Tree
Nasir Ganikhodjaev,Ashraf Mohamed Nawi,Mohd Hirzie Mohd Rodzhan 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.61 No.7
We study the phase diagrams for the Potts model with restricted competing nearest-neighbor interactions <i>J</i><sub>1</sub> and ternary interactions <i>J<sub>pt</sub></i> on a Cayley tree of arbitrary order <i>k</i>. At vanishing temperature, the phase diagram is fully determined for all values and signs of <i>J<sub>pt</sub></i>/<i>J</i><sub>1</sub> and <i>T</i>/<i>J</i><sub>1</sub>. The phase diagrams are obtained from stability conditions, and characteristic points in the iteration scheme are numerically analyzed. The wavevectors versus temperature are plotted for some critical points in the modulated phases. Then, we using the Lyapunov exponent to verify the stability of the periods.
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Potts Model with the Simplest Modulated Phase
Nasir Ganikhodjaev,Seyit Temir,Hasan Ak³n,Selman Ugu 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.59 No.5
We study the phase diagrams for the Potts model on the Bethe lattice with competing nearest-neighbor interactions J1 and ternary interactions J_p and J_t: A_t vanishing temperature, the phase diagram is fully determined for all values and signs of J_p = J_1 and J_t = J_1; in particular, we show that the phase diagrams contain ferromagnetic, paramagnetic and < 2 > phases only; <i>i.e.</i>, the set of modulated phases consists of the < 2 > phase only for J_1 > 0 and J_p = J_1 < 0: We verify that values of T = J_1 in the very narrow strip -0.11 < T = J_1 < 0 with -J_p = J_1 < 0 favor the modulated phase, which is either a commensurate phase with a very large period or an incommensurate phase. The transition lines are obtained from stability conditions, and characteristic points in the phase diagram are analyzed by using numerical iterations. Also the wavevectors versus temperature are plotted for some critical points in the modulated phases.
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