Abstract:We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions ∆ 1 and ∆ 2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively.

The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method. A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model. The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures. So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6. The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.

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Using the recursion equations technique, the influences of the single-ion anisotropies or crystal-fields interactions on the magnetic properties of the mixed spin-1 and spin-7/2 Blume-Capel (BC) Ising ferrimagnetic system are studied on the Bethe lattice (BL). The ground-state phase diagram is constructed, the thermal behaviors of the orderparameters and the free-energy are thoroughly investigated in order to characterize the nature of the phase transitions and to obtain the phase transition temperature. Then, the temperature phase diagrams are obtained in the case of equal crystal-field interactions on the (kT /|J| and D/|J|) planes when q = 3, 4 and 6 and in the case of unequal crystal-fields interactions on the (kT /|J| and D A /|J|) and (kT /|J| and D B /|J|) planes for selected values of D B /|J| and D A /|J| respectively when q = 3. The model shows first-order and second-order phase transitions, and where the lines are connected is the tricritical point. Besides the first-order and second-order phase transitions, the system also exhibits compensation temperatures depending on appropriate values of the crystalfields interactions.