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.

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The mixed spin-2 and spin-3/2 Blume-Emery-Griffiths (BEG) Ising ferrimagnetic system is studied by the Bethe lattice approach. The ground-state phase diagram is constructed. The influence of the crystal-field and the biquadratic interactions among neighboring spins on the thermal behaviors of the system is singled out. The system displays very rich critical behaviors with the existence of tricritical points. Compensation points where the global magnetization of the system vanishes have been detected for appropriate values of the system parameters.

We used mean-field theory based on the Bogoliubov inequality for the Gibbs free energy to examine the magnetic properties of a mixed spin-5/2 and spin-7/2 Blume-Capel ferrimagnetic system. The thermal behaviours of the system magnetization are classified according to the extended Néel nomenclature. The system exhibits compensation phenomena where a complete cancellation of sublattice magnetizations is observed below the critical temperature. Temperature-dependent phase diagrams are constructed for the case of unequal sublattice crystal field interactions. Under appropriate conditions, our calculations reveal first-order transitions in addition to second-order ones previously observed in Monte Carlo simulations. 1 Нацiональна вища школа енергетики та процесiв науки (ENSGEP), унiверситет м. Абомей, Республiка Бенiн 2 Iнститут математики i фiзичних наук (IMSP), Республiка Бенiн 3 Унiверситет м. Абомей-Калавi, фiзичний вiддiл, Республiка Бенiн 4 GSMC, факультет природничих наук i технологiй, унiверситет Марiана Нгуабi, Браззавiль, Конго i LMPHE, факультет природничих наук, унiверситет V Мохаммеда, Рабат, Морокко 5 Унiверситет Ерджiєс, фiзичний вiддiл, 38039, Кайсерi, ТуреччинаМи застосували середньопольову теорiю, що базується на нерiвностi Боголюбова для вiльної енергiї Гiббса, для вивчення магнiтних властивостей змiшаної спiн-5/2 i спiн-7/2 феромагнiтної системи Блюма-Капела. Температурна поведiнка намагнiченостi системи класифiкується вiдповiдно до розширеної номенклатури Нееля. Система демонструє компенсацiйне явище, де спостерiгається повне скасування намагнiченостi пiдграток нижче критичної температури. Для випадку неоднакових взаємодiй кристалiчного поля пiдграток побудовано температурно залежнi фазовi дiаграми. При певних умовах нашi обчислення виявили перехiд першого роду додатково до переходу другого роду, що був спостережений ранiше в симуляцiях Монте Карло.Ключовi слова: середньопольова теорiя, спiн-змiшана система, намагнiченiсть, компенсацiйна температура, фазовi переходи 33601-10

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