Abstract In this study, we rigorously investigate the spin-7/2 Ising Blume–Capel model subjected to randomly distributed single-ion anisotropy within a mean-field framework based on the Bogoliubov variational inequality. The ground-state phase diagram in the (, d/q α, d / q) plane reveals a rich hierarchy of magnetic phases, arising from the competition between the disorder strength α and the crystal field parameter d. At finite temperatures, the system exhibits a complex phase topology characterized by first-and second-order phase transitions, reentrant behavior, and isolated critical points. These features originate from the interplay between thermal fluctuations, anisotropy, and quenched disorder, and are significantly enhanced compared to lower-spin systems. The magnetic response displays multiple magnetization plateaus together with a pronounced multi-loop hysteresis structure, stemming from metastable states associated with the multilevel nature of the spin-7/2 system and strongly amplified by disorder effects. Overall, the results highlight the key role of high spin and quenched disorder in generating rich and nontrivial magnetic behavior.
Kake et al. (Sat,) studied this question.