We study within a mean-field approach the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Galuber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal field interaction D . We have obtained two types of solutions: a symmetric one, which corresponds paramagnetic phase where the magnetization (m) of the system oscillates in time around zero, and an antisymmetric one where m oscillates in time around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits one or more dynamic tricritical point, which depends on the values D . We also calculate the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

We present a study, within a mean-field approach, of the stationary states of the kinetic spin-3/2 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization (m) of the system oscillates in time around zero, which corresponds to a paramagnetic phase (P), and an antisymmetric one where m oscillates in time around a finite value different from zero, namely +/-3/2 and +/-1/2 that corresponds to the ferromagnetic-3/2 (F3/2) and the ferromagnetic-1/2 (F1/2) phases, respectively. There are coexistence regions of the phase space where the F3/2, F1/2, (F3/2 + F1/2), F3/2, P(F3/2 + P), F1/2, and P(F1/2 + P), F3/2, F1/2, P(F3/2 + F1/2 + P) phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, $\sigma=\pm1/2$, alternated with spins that can take the four values, $S=\pm3/2, \pm1/2$. We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude $(h)$ and reduced temperature $(T)$ plane, and in the reduced temperature and interaction parameter planes, namely in the $(h, T)$ and $(d, T)$ planes, $d$ is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in $(h, T)$ plane, but do not exhibit in the $(d, T)$ plane for low values of $h$. The dynamic multicritical point or dynamic critical end point exist in the $(d, T)$ plane for low values of $h$. Moreover, phase diagrams contain paramagnetic $(p)$, ferromagnetic $(f)$, ferrimagnetic $(i)$ phases, two coexistence or mixed phase regions, $(f+p)$ and $(i+p)$, that strongly depend on interaction parameters.Comment: 13 pages, 6 figures, submitted to Journal of Magnetism and Magnetic Material

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.

A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 .