Abstract
In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of phases and partition functions corresponding to the model are rigorously studied. Exact solutions of the mentioned model are compared with the numerical results given in Ganikhodjaev et al. [J. Concr. Appl. Math., 2011, 9, No. 1, 26-34].
Highlights
In magnetic and ferroelectric systems, phase diagrams of a model with various transition lines and modulated phases are obtained with the presence of different competing interactions [1]
In references [2, 5, 7], some features of complex phase diagrams corresponding to the ANNNI (Axial Next-Nearest-Neighbor Ising) model consisting of an Ising spin Hamiltonian on a Cayley tree were studied
Many authors have plotted the phase diagrams associated with the model by means of the periodic fixed points of an operator consisting of recurrent relations [2, 4, 5, 8,9,10,11,12, 17]
Summary
In magnetic and ferroelectric systems, phase diagrams of a model with various transition lines and modulated phases are obtained with the presence of different competing interactions [1]. Azhari et al [20] investigated the magnetic properties of the mixed spin-1/2 and spin-1 Ising ferromagnetic system with four-spin interaction J4 and next-nearest neighbor (NNN) coupling J0. They are interested in the phase diagram and in the location and the multitude of the compensation point. In [4], we numerically studied the Lyapunov exponent and modulated phases for the Ising model with different coupling constants on an arbitrary-order Cayley tree.
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