We have presented dynamic phase transition features and stationary-state behavior of a ferrimagnetic small nanoparticle system with a core-shell structure. By means of detailed Monte Carlo simulations, a complete picture of the phase diagrams and magnetization profiles have been presented and the conditions for the occurrence of a compensation point Tcomp in the system have been investigated. According to Néel nomenclature, the magnetization curves of the particle have been found to obey P-type, N-type and Q-type classification schemes under certain conditions. Much effort has been devoted to investigation of hysteretic response of the particle and we observed the existence of triple hysteresis loop behavior which originates from the existence of a weak ferromagnetic core coupling Jc/J sh , as well as a strong antiferromagnetic interface exchange interaction Jint/J sh . Most of the calculations have been performed for a particle in the presence of oscillating fields of very high frequencies and high amplitudes in comparison with exchange interactions which resembles a magnetic system under the influence of ultrafast switching fields. Particular attention has also been paid on the influence of the particle size on the thermal and magnetic properties, as well as magnetic features such as coercivity, remanence and compensation temperature of the particle. We have found that in the presence of ultrafast switching fields, the particle may exhibit a dynamic phase transition from paramagnetic to a dynamically ordered phase with increasing ferromagnetic shell thickness.

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The magnetic properties of a spin-1 Blume-Capel (BC) model on a square lattice (q = 4) with a ferromagnetic interaction have been examined here by the use of Monte Carlo (MC) simulation technique and an introduced effective-field approximation (IEFT), which includes the correlations between different spins that emerge when expanding the identities. The effects of the external magnetic field and crystal field on the magnetic properties of the spin system are discussed in detail. In order to obtain credible results, a detailed comparison of the results obtained by the two methods has been made with those of the other methods in the literature. A number of interesting phenomena originating from the temperature, crystal field and external field have been found.

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An Ising model with quenched random magnetic fields is examined for single-Gaussian, bimodal, and double-Gaussian random-field distributions by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random-field distribution shape dependencies of the phase diagrams and magnetization curves are investigated for simple cubic, body-centered-cubic, and face-centered-cubic lattices. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail.