Exact Recursion Relations Study of Critical Behaviors, Compensation Temperatures and Multi-Hysteresis in the Mixed Spin-(3 / 2 , 9 / 2) Blume-Capel Ferrimagnetic Model on the Bethe Lattice

Abstract

The mixed spin-(3 / 2 , 9 / 2) Blume-Capel ferrimagnetic model is investigated on the Bethe lattice using exact recursion relations (ERR). Ground-state phase diagrams in the ( D A / q | J | , D B / q | J | ) plane reveal ten competing ferrimagnetic configurations and seven multicritical points—two more ground-state regions than in the previously studied (3 / 2 , 7 / 2) case on the same lattice. Temperature-dependent phase diagrams are constructed in the ( D A / | J | , k T / | J | ) , ( D B / | J | , k T / | J | ) planes and in the isotropic case DA = DB = D , for coordination numbers q = 3 , 4 , 5 , 6. The system exhibits both first- and second-order phase transitions and compensation temperatures for appropriate crystal-field values. Under an external magnetic field, the model displays single, double, and triple hysteresis loops; triple loops occur for ? 0.6 ≤ J / | J | ? 0.5 . The ten competing spin states of sublattice B (versus eight for spin-7 / 2) generate nine independent recursion ratios, a richer fixed-point structure, systematically higher critical temperatures, and a broader multi-hysteresis parameter range—features that are not recoverable by simple extrapolation from the lower-spin case. Results are compared with mean-field studies of the same spin pair on the simple cubic lattice and with the (3 / 2 , 7 / 2) Bethe lattice.