Reentrant phenomenon in a transverse spin-1 Ising nanoparticle with diluted magnetic sites

In the present work, we have examined the influence of surface shell exchange coupling on the magnetic properties of a diluted ferromagnetic spin- 1 Ising nanocubic particle, by employing the effective-field theory with correlations based on the probability distribution technique. Some interesting results have been found such as, a tricritical point, a triple point, an isolated critical point, reentrant and even double reentrant phenomena, S-, R- and Q-type behaviors, as well as, both first- and second-order phase transitions as it is confirmed by the free energy. In addition, when the interactions are low between the surface shell sites, quadruple hysteresis loops can be seen in the system.