Repulsive Biquadratic Coupling Research Articles

Phase Diagrams of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

Phase Diagrams of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

The phase diagrams with influence of biquadratic exchange coupling on martensitic–austenitic transformations for core–surface nanoparticles

Recently, origin of the martensite–austenite transitions in core–surface type magnetic nanoparticles has been investigated theoretically and it has been indicated that repulsive biquadratic exchange coupling (K<0.0) causes the coexisting martensite and austenite phases. In the present paper, the phase diagrams of homogeneous and composite nanoparticles in the kBT/J0−D/J0 plane are studied for the presence and absence of attractive biquadratic exchange interaction in addition to repulsive biquadratic exchange interaction. Significant changes in the phase diagram points are discussed in the presence of martensitic and austenitic transformations. Four regions in the phase diagrams are found as second-order, martensitic–austenitic, TCid and first-order phase transition regimes.

Multicritical Dynamic Phase Diagrams and Dynamic Hysteresis Loops in a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Repulsive Biquadratic Coupling: Glauber Dynamic Approach

The stationary states of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system with repulsive biquadratic coupling are examined within a mean-field approach under the presence of a time varying (sinusoidal) magnetic field. We employ Glauber-type stochastic dynamics to construct a set of coupled mean-field dynamic equations, and we solve these equations to find the phases in the system. We also investigate the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transitions (DPTs) and obtain the DPT points. The phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane, and a comparison is made with the results of other kinetic mixed spin systems. We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties, and we find the results are in good agreement with some previous theoretical and experimental works.

A renormalization-group analysis of a spin-1 Ising ferromagnet with competing crystal-field and repulsive biquadratic interactions

Phase diagrams have been produced and critical exponents calculated for a Blume–Emery–Griffiths system with competing biquadratic and crystal-field interactions with uniform ferromagnetic bilinear interactions. This competition directly effects the clustering and density of nonmagnetic impurities. These results have been produced using renormalization-group methods with a hierarchical lattice. A series of planes of constant, repulsive biquadratic coupling have been probed while varying the temperature and concentration of annealed vacancies in the system. The sinks have been analyzed and interpreted, and critical exponents calculated for the higher order transitions.

Dynamic Phase Transition and Multicritical Dynamic Phase Diagrams of The Kinetic Spin-2 Ising Model With Repulsive Biquadratic Coupling under a Time-dependent Oscillating External Field

Dynamic Phase Transition and Multicritical Dynamic Phase Diagrams of The Kinetic Spin-2 Ising Model With Repulsive Biquadratic Coupling under a Time-dependent Oscillating External Field

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.

Dynamic phase transition and multicritical dynamic phase diagrams of the kinetic spin-3/2 Blume–Emery–Griffiths model with repulsive biquadratic coupling under a time-dependent oscillating external field

We extend our recent paper [O. Canko, B. Deviren, M. Keskin, J. Phys.: Condens. Mater 118 (2006) 6635] to present a study, within a mean-field approach, the stationary states of the kinetic spin-3/2 Blume–Emery–Griffiths model with repulsive biquadratic interaction under the presence of a time varying (sinusoidal) magnetic field. We found that the dynamic phase diagrams of the present work exhibit more complex, richer and more topological different types of phase diagrams than our recent paper. Especially, the obtained dynamic phase diagrams show the ferrimagnetic ( i) phase in addition to the ferromagnetic ± 3 / 2 ( f 3 / 2 ), ferromagnetic ± 1 / 2 ( f 1 / 2 ), antiquadrupolar or staggered ( a) and disordered ( d) phases, and the f 3 / 2 + i , f 1 / 2 + d , i + d , f 3 / 2 + i + d , a + d and/or f 3 / 2 + i + a coexistence regions in addition to the f 3 / 2 + f 1 / 2 , f 3 / 2 + d , f 3 / 2 + a , f 1 / 2 + d and/or f 3 / 2 + a + d coexistence regions, depending on interaction parameters. Moreover, the phase diagrams exhibit dynamic zero-temperature critical, critical end, double critical end, multicritical, and/or pentacritical special points in addition to the dynamic tricritical, double critical end point, triple, quadruple and/or tetracritical special points that depending on the interaction parameters.

Multicritical phase diagrams of the ferromagnetic spin- [formula omitted] Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: The cluster variation method and the path probability method with the point distribution

We study the thermal variations of the ferromagnetic spin- 3 2 Blume–Emery–Griffiths (BEG) model with repulsive biquadratic coupling by using the lowest approximation of the cluster variation method (LACVM) in the absence and presence of the external magnetic field. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states. We also study the dynamics of the model by using the path probability method (PPM) with the point distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagrams in addition to the equilibrium phase diagrams in the ( kT/ J, K/ J) and ( kT/ J, D/ J) planes. It is found that the metastable phase diagrams always exist at the low temperatures, which are consistent with experimental and theoretical works.

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.

Multicritical behavior of the antiferromagnetic Blume–Emery–Griffiths model with the repulsive biquadratic coupling in an external magnetic field

We have studied the antiferromagnetic Blume–Emery–Griffiths model with the repulsive biquadratic coupling in an external magnetic field using the lowest approximation of the cluster variation method which is identical to the mean-field approximation. First, we have investigated the thermal variations of the sublattice magnetizations and obtained four different main topological types. Then, we have calculated the phase diagrams and five main different phase diagram topologies are found. Finally, the discussion and comparison of the phase diagrams are made.

Multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution

As a continuation of the previously published work, the pair approximation of the cluster variation method is applied to study the temperature dependences of the order parameters of the Blume–Emery–Griffiths model with repulsive biquadratic coupling on a body centered cubic lattice. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. We study the dynamics of the model by the path probability method with pair distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagram in addition to the equilibrium phase diagram and also the first-order phase transition line for the unstable branches of the quadrupole order parameter is superimposed on the phase diagrams. It is found that the metastable phase diagram and the first-order phase boundary for the unstable quadrupole order parameter always exist at the low temperatures which are consistent with experimental and theoretical works.

The spin‐3/2 Blume–Emery–Griffiths model with repulsive biquadratic coupling in an external field

AbstractThe spin‐3/2 Blume–Emery–Griffiths model is solved on the Bethe lattice in the absence and presence of the external field using the iteration technique (recursion method). The phase diagrams are obtained for the coordination number q = 3, 4, 6 and 8. We confirm the existence of a staggered quadrupolar phase in addition to a ferrimagnetic and ferromagnetic ordered phases and analyze the occurence of re‐entrant boundaries inside the ordered region as a character of the coordination of the lattice. A comparison is made with the results of other approximate methods. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Multicritical phase diagrams of the Blume-Emery-Griffiths model with repulsive biquadratic coupling including metastable phases

We investigate the thermal variations of the spin-1 Blume-Emergy-Griffiths model with the repulsive biquadratic interaction by using the lowest approximation of the cluster-variation method. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable, and unstable states is made by comparing the free-energy values of these states. We also study the dynamics of the model by the path probability method in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. This is done by studying the relaxation of the order parameters and as well as expressing the solution of the dynamic equations by means of the flow diagrams. Finally, we present the metastable phase diagrams in addition to the equilibrium phase diagrams in $(kT/J,D/J)$ and $(kT/J,K/J)$ planes.

Blume-Emery-Griffiths model on the square lattice with repulsive biquadratic coupling

Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K > 0 are compared with other renormalization group calculations and with exact results, in order to assess the magnitude of the errors introduced by our approximate calculation. The quantitative agreement is excellent; values for critical parameters differ, in some cases, by less than 1% from exact ones. For K < 0, our results lead to a rich phase diagram, with antiquadrupolar and ferromagnetic ordered phases. Contrarily to Monte Carlo simulations, these two phases meet only at zero temperature. Both antiquadrupolar-disordered and ferromagnetic-disordered transitions are found to be continuous and no ferrimagnetic phase is found.

Dimensionality effects on the multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling: Mean-field and renormalization-group studies

Six new phase diagrams, including a novel multicritical topology and two new ordered phases, are obtained by the global mean-field theory of the spin-1 Ising model with only nearest-neighbor interactions, for negative biquadratic couplings. Renormalization-group studies indicate a threshold spatial dimension, above and below which different sequences of phase diagrams occur.