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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.
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.