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The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethelattice in the presence of a magnetic field $h$ via the recursion relationsmethod. A ground-state phase diagram is constructed which may be needful toexplore important regions of the temperature phase diagrams of a model. Theorder-parameters, the corresponding response functions and internal energy arethoroughly investigated in order to typify the nature of the phase transitionand to get the corresponding temperatures. So, in the absence of the magneticfield, the temperature phase diagrams are displayed in the case of an equalcrystal-field on the $(k_{\textrm{B}}T/|J|, \,D/|J|)$ plane when $q=3,4$, $5$and $6$. The model only exhibits the second-order phase transition forappropriate values of physical parameters of a model.

Bethe approach study of the mixed spin-1/2 and spin-5/2 Ising system in the presence of an applied magnetic field