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The African review of physics

THE MIXED SPIN-1 AND SPIN-5/2 BEG MODEL IN A STAGGERED MAGNETIC FIELD

Joel Kple, R. A. A. Yessoufou, Félix Hontinfinde

Published Oct 26, 2012• 1 citation
OpenAlex

Abstract

The mixed spin-1 and spin5 2 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction (D) is investigated by means of recursion relations on the Bethe lattice in the presence of a staggered magnetic field. The interactions are assumed to be only between nearestneighbors. The competition between model parameters leads to very rich T=0 phase diagrams which may be useful to explore interesting domains of the finite-temperature phase diagrams of the model. Some thermal properties of the system are presented. The magnetization is also described by numerical simulations of the model on a square lattice using Glauber stochastic dynamics in the presence of an oscillating external staggered field. Our present results bear little resemblance to those previously reported on various kinetic Ising systems obtained by integrating differential equations.

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The mixed spin-1 and spin5 2 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction (D) is investigated by means of recursion relations on the Bethe lattice in the presence of a staggered magnetic field. The interactions are assumed to be only between nearestneighbors. The competition between model parameters leads to very rich T=0 phase diagrams which may be useful to explore interesting domains of the finite-temperature phase diagrams of the model. Some thermal properties of the system are presented. The magnetization is also described by numerical simulations of the model on a square lattice using Glauber stochastic dynamics in the presence of an oscillating external staggered field. Our present results bear little resemblance to those previously reported on various kinetic Ising systems obtained by integrating differential equations.
We present a study, within a mean-field approach, of the kinetics of the mixed spin-1 and spin-3/2 Ising model Hamiltonian with bilinear and biquadratic nearest-neighbor exchange interactions and a single-ion potential or crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the time dependence of average magnetizations and the quadrupole moments, and the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points and construct the phase diagrams in three different planes. Phase diagrams contain disordered (d) , ferrimagnetic (i) , the antiquadrupolar or staggered (a) phases, and four coexistence or mixed phase regions, namely, the i+d , i+a , i+a+d , and a+d , that strongly depend on interaction parameters. The system also exhibits the dynamic tricritical behavior in most cases, the reentrant behavior in few cases.
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The spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed and full set of phase diagrams are constructed for both positive and negative biquadratic couplings. In latter case we observe all remarkable features of the model, uncluding doubly-reentrant behavior and ferrimagnetic phase. A comparison with the results of other approximation schemes is done.
The mixed spin-2 and spin-3/2 Blume-Emery-Griffiths (BEG) Ising ferrimagnetic system is studied by the Bethe lattice approach. The ground-state phase diagram is constructed. The influence of the crystal-field and the biquadratic interactions among neighboring spins on the thermal behaviors of the system is singled out. The system displays very rich critical behaviors with the existence of tricritical points. Compensation points where the global magnetization of the system vanishes have been detected for appropriate values of the system parameters.
Kinetics of the mixed spin (1, 3/2) Ising ferrimagnetic system on the two interpenetrating square lattices with the bilinear and crystal-field interactions under an oscillating magnetic field were investigated by using the path probability method (PPM). We examined time variations in average dynamic magnetizations and obtained phases and then we investigated the thermal behaviors of dynamic magnetizations to determine the nature of the dynamic phase transitions and find their temperature values. We also constructed the dynamic phase diagrams in (d,T) and (h_0,T) planes. Dynamic phase diagrams display the paramagnetic (p), ferrimagnetic (i), and mixed phases (i+p), and one dynamic tricritical point and dynamic double critical endpoints. We found that the PPM is a more convenient method to investigate the kinetics and dynamics behaviors of ferrimagnetism.
The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method.A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model.The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures.So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6.The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.