The magnetic and thermal properties of a ferrimagnetic mixed spin-1 and spin-2 cubic Ising nanowire are studied by using the Monte Carlo simulation. The influences of the nearest (JAB) and next-nearest neighbor (JA and JB) exchange interactions and the single-ion anisotropies (DA and DB) on the critical and compensation temperatures are illustrated. Moreover, the phase diagrams on the (temperature, anisotropy) plane are plotted for several values of JA/|JAB|. The system shows very rich and interesting behaviors, namely first and second order phase transitions, tricritical points and compensation phenomenon. Finally, the dependence of hysteresis loops on the anisotropies, the exchange interactions and the temperature is also investigated.

Using Monte Carlo simulation and mean field approximation, we studied the magnetic properties of spin-3/2 chain with hexagonal spin-1/2 shell and negative core-shell exchange coupling. The obtained results show that the spins 3/2 in the core have an important influence on the magnetic behavior of the system such as the appearance of compensation temperatures as well as first- and second-order phase transitions. Moreover, we investigated the effects of exchange interactions and anisotropy on the phase diagrams of the system.

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By the use of the Migdal–Kadanoff renormalization group technique and the mean field approximation, we have explored the critical behavior of the semi-infinite mixed spin-7/2 and spin-1/2 Blume–Capel model. As a function of the computation ratios (bulk-surface) R and Y, different phase diagrams in the bulk and on the surface are classified and determined in the (surface anisotropy, temperature) plane. We have found four types of phase diagrams characterized by ordinary, extraordinary, surface, and special phase transitions. The derivative of the free energy and the behavior of the bulk and surface magnetizations are plotted at very low temperatures proving the existence of first-order transitions for both the surface and bulk. We have also presented the related fixed points and the critical exponents manifesting several classes of universality at the surface. Otherwise, a comparison was made between the two methods as well as with previous studies.