Magnetic Properties of the Ferrimagnetic Blume-Capel Model with Mixed Spin-52 and Spin-3: Exact Recursion Relations Approach

We employ the exact recursion relations to investigate the magnetic properties of a ferrimagnetic Blume-Capel model composed of mixed spins 5/2 and 3 on the Bethe lattice, considering only nearest-neighbor interactions. The ground state phase diagrams are constructed in the (DA/q|J|, DB/q|J|) plane, revealing multiple possible ground states, multiphase points, and phase boundaries. Temperature-dependent phase diagrams are systematically derived for various single-ion anisotropies, demonstrating a wide range of critical phenomena, including first-and second-order phase transitions, tricritical points, compensation temperatures, and reentrant behavior in the absence of a magnetic field. Notably, the system exhibits up to four distinct compensation temperatures depending on the values of the crystal field parameters. Additionally, under an applied magnetic field, the system exhibits complex hysteresis behaviors, including single, double, and triple hysteresis loops, which emerge for specific parameter regimes. These findings underscore the intricate interplay between anisotropy, thermal fluctuations, and external field in governing the magnetic response of mixed-spin ferrimagnetic systems.