Systematic investigation of dynamic magnetic phase behavior using the path probability method: Mixed-Spin (1,7/2) Blume-Capel Ising system on a hexagonal lattice under an oscillating magnetic field

The dynamic magnetic phase behavior of a mixed-spin (1,7/2) Blume-Capel Ising system on a hexagonal lattice is investigated using the Path Probability Method in the presence of a periodically oscillating magnetic field. The effects of the magnetic-field amplitude and crystal-field interaction on the dynamic order parameters and phase diagrams are examined systematically for both ferrimagnetic (J AB < 0) and ferromagnetic (J AB > 0) exchange regimes. Thermal variations in dynamic magnetizations are used to determine the phase-transition temperatures and the nature of the transitions. Dynamic phase diagrams constructed in the (T, h 0 ) and (T, d) planes reveal first-order and second-order dynamic phase transitions, tricritical points, and parameter-dependent phase boundaries. Various Néel-type compensation behaviors are observed in the ferrimagnetic regime, whereas no compensation phenomenon occurs in the ferromagnetic case. The results demonstrate that competition among exchange interactions, crystal-field effects, thermal fluctuations, and the oscillating magnetic field strongly influences the stability of the dynamically ordered phases and the topology of the phase diagrams. The present study provides a systematic dynamic phase-diagram analysis of the mixed-spin (1,7/2) Blume-Capel system on a hexagonal lattice within the PPM framework.