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The magnetic properties of the mixed spin ... and spin ... Ising model with a crystal-field in a longitudinal magnetic field are investigated on the Bethe lattice using exact recursion relations. The ground-state phase diagram is constructed. The temperature-dependent one is displayed in the case of uniform crystal-field on the (kgT/|J|, D/|J|) plane in the absence of the external constraint for lattice coordination numbers z = 3,4, 6. The order parameters and corresponding response functions as well as the internal energy are calculated and examined in detail in order to feature the real nature of phase boundaries and corresponding temperatures. The thermal variations of the average magnetization are classified according to the Neel nomenclature. [ABSTRACT FROM AUTHOR]

The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spin- S (S > 1=2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations. In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations. It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer. [ABSTRACT FROM AUTHOR]