Magnetic properties and hysteresis behaviors of a graphyne core/shell nanoparticles are studied within the framework of Monte carlo calculations. We analyze in detail the ground-state phase diagrams in different planes. We examine the effects of the extrinsic and intrinsic parameters of the Hamiltonian on the magnetic and thermodynamic quantities of the system, namely, the total magnetization, its corresponding susceptibility, the hysteresis curves, and the compensation behavior that is of crucial importance for technological applications such as thermo-optical recording. A number of characteristic behaviors are found, such as the occurrence of one and two compensation temperatures and the existence of two new and non-classified types of compensation behavior in addition to the Q-, P- and N-types. Moreover, single and triple hysteresis loops, which exhibit different step effects and various shapes, are observed.

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