We study a quantum Carnot and Otto engine consisting of two coupled spin- \(\frac{1}{2}\) particles and two coupled spin-1 particles within the Ising model, focusing on how the system transitions between functioning as a heat engine or a refrigerator based on the external magnetic fields and coupling constant. The magnetic fields influence the energy levels of the spins, while the coupling constant governs the strength of spin interactions, enabling enhanced energy transfer and utilization. Our analysis reveals that the coupled system achieves higher efficiency and coefficient of performance (COP) compared to its uncoupled counterpart under specific conditions. By identifying optimal values for the magnetic fields and coupling constant, we demonstrate how the interplay of these parameters allows the coupled system to outperform uncoupled systems in both energy conversion and thermal regulation, highlighting the potential of spin coupling in optimizing quantum thermodynamic devices.
