TITLE:
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
AUTHORS:
Sènan Ida Valérie Hontinfinde, Brice Bonaparte Adjalla, Bignon Si Jean-Eudes Natabou
KEYWORDS:
Blume-Capel Model, Mixed Spin, Bethe Lattice, Exact Recursion Relations, Compensation Temperature, Multi-Hysteresis, Phase Transition
JOURNAL NAME:
World Journal of Condensed Matter Physics,
Vol.16 No.2,
June
30,
2026
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 |
,
kT/
| J |
)
,
(
D
B
/
| J |
,
kT/
| 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.