Systematic Investigation of Dynamic Magnetic Phase Transitions Using the Path Probability Method. III. Mixed-Spin (3/2,7/2) Blume-Capel Ising System on a Square Lattice under an Oscillating Magnetic Field

The dynamic magnetic properties of the mixed-spin (3/2,7/2) Blume-Capel Ising system on an interpenetrating square lattice are investigated using the path probability method in the presence of a time-dependent oscillating magnetic field. The thermal variations of the dynamic magnetizations, stationary magnetization oscillations, compensation behavior, and dynamic phase diagrams are examined for both errimagnetic and ferromagnetic exchange interactions. The system exhibits dynamically ordered and disordered phases separated by first- and second-order dynamic phase transition lines, together with dynamic tricritical points. For the ferrimagnetic case, coexistence regions and P-, Q-, R-, S-, and N-type compensation behaviors are observed, whereas W-, or M-type characteristics are absent within the investigated parameter ranges. Increasing the crystal-field interaction stabilizes the ordered phase, while increasing the magnetic-field amplitude promotes dynamic disordering and bistability. In contrast, the ferromagnetic case exhibits a simpler phase structure, with broader ordered regions, weaker coexistence effects, and no compensation behavior. The results demonstrate that the interplay among exchange interactions, crystal-field interactions, and oscillating magnetic field governs the nonequilibrium phase topology and dynamic critical behavior of the mixed-spin (3/2,7/2) system.