Quantum stirling heat engines with a three-spin LMG model: Performance and thermodynamic modes under anisotropic coupling

The quantum thermodynamic performance of a Stirling cycle employing a three-spin Lipkin-Meshkov-Glick (LMG) model is investigated under varying magnetic interaction anisotropies and control parameters. The model operates in the anisotropic XY regime (γ=+1), the Ising limit (γ=0), and the mixed ferromagnetic regime (γ=−1), with key thermodynamic quantities evaluated across a range of temperature ratios, magnetic field strengths, and coupling asymmetries. The mean energy landscape reveals a strong dependence on the anisotropy parameter, highlighting quantum coherence effects and spin alignment. The operational phase space is mapped, showing distinct transitions between heat engine, refrigerator, and heater modes, with γ=+1 exhibiting the broadest mode diversity and γ=−1 yielding robust engine-like behavior. Thermodynamic quantities such as heat exchange and work output are analyzed, showing mode transitions driven by magnetic field tuning. Efficiency, refrigeration performance (ε), and the refined performance coefficient (Π) are presented, revealing intricate dependencies on system parameters. Anisotropic spin coupling is shown to enhance thermodynamic responsiveness, while strong magnetic fields induce saturation and performance decline due to level polarization. The results demonstrated that quantum many-body interactions, when properly tuned, could be harnessed to optimize the design of nanoscale heat engines, refrigerators, and other quantum thermal devices.