Dynamic phase transition in the kinetic spin-2 Blume–Emery–Griffiths model in an oscillating field

We extend our recent paper [M. Keskin, O. Canko, M. Erta?, J. Exp. Theor. Phys. (Sov. Phys. JETP) 105 (2007) 1190.] to present a study, within a mean-field approach, the stationary states of the kinetic spin-2 Blume–Emery–Griffiths model in the presence of a time-dependent oscillating magnetic field by using the Glauber-type of stochastic dynamics. We found 20 fundamental types of dynamic phase diagrams where exhibit more complex and richer phase diagrams than our recent paper. Especially, the obtained dynamic phase diagrams show the dynamic triple, quadruple and dynamic double critical end points besides dynamic tricritical points that depending on interaction parameters. The phase diagrams also exhibit a disordered (d) and the ferromagnetic-2 (f₂) phases, and the f₂+d, f₂+fq, fq+d, f₂+f₁+fq and f₂+fq+d, where f₁ are fq the ferromagnetic-1 and ferroquadrupolar or simply quadrupolar phases respectively, coexistence phase regions that strongly depend on interaction parameters.     

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 in the kinetic spin-5/2 Blume–Emery–Griffiths model in an oscillating external magnetic field

Employing a mean-field approach, we study the stationary states of the kinetic spin-5/2 Blume–Emery–Griffiths (BEG) model under the presence of a time-varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. We employ the Glauber transition rates to construct the set of dynamic mean-field equations. We investigate the time variation in average order parameters to find the phases in the system, and the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transtions and to the dynamic phase transition temperature. The dynamic phase diagrams are presented in three different planes. The phase diagrams contain the ferromagnetic-5/2, the ferromagnetic-3/2, the ferromagnetic-1/2, the ferroquadrupolar, and disordered fundamental phases. They also include the nine coexisting or mixed phases composed of binary and ternary combinations of fundamental phases that strongly depend on the interaction parameters. The phase diagrams display the critical end point, double critical end point, triple point, quadruple point, and one, two, or three special points and the dynamic tricritical point that depends on the interaction parameters.     

Dynamic phase transition and dynamic phase diagrams in the spin-5/2 Blume–Capel model under a time-dependent oscillating external field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model under the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the mean-field dynamic equation. Then, we study the time variation of the average magnetization to find the phases in the system. We also investigate the behaviour of the dynamic magnetization to characterize the nature (continuous and discontinuous) of transition and to obtain the DPT points. We present the dynamic phase diagrams in two different planes. The phase diagrams include the ferromagnetic-5/2 (f_5/2), the ferromagnetic-1/2 (f_1/2) and paramagnetic (p) fundamental phases. In addition to these fundamental phases, we find 10 mixed phases, depending on the interaction parameters. The phase diagrams display many special points, such as a dynamic tricritical point, a double critical end point, a triple point and a quadruple point.     

Multicritical behaviors of the antiferromagnetic Blume–Emery–Griffiths model with the external magnetic field on the Bethe lattice

The antiferromagnetic Blume–Emery–Griffiths model in an external magnetic field is studied by using the exact recursion relations on the Bethe lattice for arbitrary values of biquadratic and for negative values of bilinear interactions. We have studied the thermal variations of two-sublattice magnetizations belonging to spin-1 BEG model to obtain the phase diagrams on the (H/|J|,kT/|J|)$(H/|J|,\mathit{kT}/|J|)$ plane. As a result, we have found that the system presents second- and first-order phase transitions, therefore, tricritical points for appropriate values of K/|J|$K/\left|J\right|$, D/|J|$D/\left|J\right|$ and q  . We have also found that the second-order phase transition lines exhibit reentrant phenomena in temperature, besides it also shows reentrant phenomena for the first-order phase lines in external magnetic field for q=4$q=4$ and 6.     

Rates of Convergence in the Blume–Emery–Griffiths Model

We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature $\beta $ and the interaction strength $K$ . The rates of convergence results are obtained as $(\beta ,K)$ converges along appropriate sequences $(\beta _n,K_n)$ to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein’s method for normal and non-normal approximation avoiding the use of transforms and supplying bounds, such as those of Berry–Esseen quality, on approximation error.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

Monte Carlo simulations of dynamic phase transitions in ultrathin Blume–Capel films

Dynamic phase transition phenomena in ultrathin films described by the Blume–Capel model have been investigated using Monte Carlo simulations. Hysteresis loops, micromagnetic structures, and hysteresis loop area curves, as well as dynamic correlation between the magnetization and the external field have been studied as functions of the field, as well as the film parameters. The variation of critical coupling of the modified film surface at which the transition temperature becomes independent of film thickness has been clarified for varying system parameters. Frequency dispersion of hysteresis loop area has been found to obey a power law for low and moderate frequencies for both ordinary and enhanced surfaces.     

Random-bond and random-anisotropy effects in the phase diagram of the Blume–Capel model

We report on Monte Carlo studies of the influence of quenched randomness on the phase diagram of the three-dimensional (3D) Blume–Capel model. The randomness is supposed to act either on the exchange coupling constants (bond randomness) or on the anisotropy distribution. With increasing disorder, first-order phase transitions are shown to change into second-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. We have also calculated critical exponents at some points in the second-order phase region which show a change of universality class in agreement with the Harris criterion.     

Metastability in the Spin-1 Blume–Emery–Griffiths Model within Constant Coupling Approximation

In this paper, the equilibrium properties of spin-1 Blume–Emery–Griffiths model are studied by using constant-coupling approximation. The dipolar and quadrupolar order parameters, the stable, metastable and unstable states and free energy of the model are investigated. The states are defined in terms of local minima of the free energy of system. The numerical calculations are presented for several values of exchange interactions on the simple cubic lattice with q = 6.     

Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field

Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field (h)$(h)$ on simple cubic lattice are studied by using the effective field theory. In the m−T$m-T$ plane, the degeneracy of the magnetization (m)$(m)$ is affected by the concentration of bond or crystal field dilution at low temperature (T)$(T)$. The magnetization curves can appear to fluctuate in certain regions of negative crystal field. In the m−h$m-h$ plane, the initial magnetization curve has an irregular behavior due to the introduction of bond dilution. The crystal field dilution has the influence on the process of magnetic domain displacement. In the χ−h$\chi -h$ plane, there exists one susceptibility (χ)$(\chi )$ shoulder and one step for different negative crystal field. The susceptibility curve takes on the feature of multi-peaks distribution under bond and crystal field dilution conditions.     

Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal–Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume–Emery–Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal–Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered.     

Mössbauer study of dynamic and phase transitions in an aqueous film–nanoclay surface system

Phase transitions in aqueous films adsorbed in clays are studied and reported for the first time. Analysis of spectral parameters allows the orto/spin-isomer pair ratio in frozen water to be established, and the Mössbauer probes to be localized on the alumosilicate surface. The temperature transformation of the spectra is explained using models that qualitatively describe first- and second-order phase transitions.     

Grassmann phase space theory and the Jaynes–Cummings model

The Jaynes-Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n$n$-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes-Cummings model based on expanding the state vector in terms of products of atomic and n$n$-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects.     

Influence of transverse field on the spin-3/2 Blume–Capel model on rectangular lattice

Transverse field effect on thermodynamic properties of the spin-3/2 Blume–Capel model on rectangular lattice in which the interactions in perpendicular directions differ in signs is studied within the mean field approximation. Phase diagrams in the (transverse field, temperature) plane are constructed for various values of single-ion anisotropy.