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Using Monte Carlo simulations, we studied phase diagrams and magnetic properties of a ferromagnetic/antiferromagnetic Ising nanoparticles assembly with the spin-1/2 core and spin-3/2 shell. The system consists of nanocubes with equivalent exchange couplings of core and shell. However, the exchange couplings between the adjacent spins of the core and shell and between the nanocubes are assumed to vary. Thus, the effects of the exchange couplings and the system size on the phase diagrams are analyzing. Interesting behaviors are found when investigating the critical behavior of the system, the magnetizations, the magnetic susceptibility and the hysteresis loops. The increase of the core/shell size involves that of the temperature one. In addition, the increase in positive exchange interactions between the spins of the core and shell, on the one hand, and between the nanocubes, on the other hand, also increase the critical temperature, which favors the stable phase (3/2, 1/2). • Monte Carlo Simulation is used to study the magnetic properties of an assembly of cubic Core-Shell nanoparticles. • Phases diagrams of critical temperature with the exchange interactions and anisotropy parameter have been studied. • The increase of positive J2/J1 and J4/J1 increase the critical temperature, favoring the stable phase (3/2, 1/2). • Core and Shell sizes, anisotropy and interactions parameters effects on Magnetic hysteresis cycles are given. • Dependent coercivity with sizes and parameters of interactions are found. [ABSTRACT FROM AUTHOR]