Critical, compensation and hysteresis behaviors studies in the ferrimagnetic Blume-Capel model with mixed half-integer spin-(3/2, 7/2): Exact recursion relations calculations

TL;DR

This study uses exact recursion relations to analyze the phase transitions, hysteresis, and magnetic properties of a mixed-spin ferrimagnetic Blume-Capel model on the Bethe lattice, revealing complex behaviors and phase diagrams.

Contribution

It provides a detailed analysis of the mixed-spin Blume-Capel ferrimagnetic system using exact recursion relations, including phase diagrams and hysteresis behaviors, which is a novel application for this model.

Findings

Identification of first- and second-order phase transitions.

Observation of multi-hysteresis cycles under external magnetic field.

Determination of remanent magnetization and coercive fields.

Abstract

The exact recursion relations are used to study the mixed half-integer spin-(3/2, 7/2) Blume-Capel Ising ferrimagnetic system on the Bethe lattice. Ground-state phase diagrams are computed in the $({D_{A}}/{q|J|}, {D_{B}}/{q|J|})$ plane to reveal different possible ground states of the model. Using the thermal changes of the order-parameters, interesting temperature dependent phase diagrams are constructed in the ($D_{A}/|J|$, $kT/|J|$), ($D_{B}/|J|$, $kT/|J|$) planes as well as in the ($D/|J|$, $kT/|J|$) plane where $D=D_A=D_B$. It is revealed that the system exhibits first- and second-order phase transitions and compensation temperatures for specific model parameter values. Under the constraint of an external magnetic field, the model also produces multi-hysteresis behaviors as single, double and triple hysteresis cycles. Particularly, the impacts of the ferrimagnetic coupling $J$ on the remanent magnetization and the coercitive fields for selected values of the other physical parameters of the system are pointed out. Our numerical results are qualitatively consistent with those reported in the literature.