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The magnetic properties of the mixed spin-$\frac{1}{2}$ andspin-$\frac{7}{2}$ Ising model with a crystal-field in a longitudinal magneticfield are investigated on the Bethe lattice using exact recursion relations.The ground-state phase diagram is constructed. The temperature-dependent one isdisplayed in the case of uniform crystal-field on the $(k_{\text{B}}T/|J|,D/|J|)$ plane in the absence of the external constraint for latticecoordination numbers $z = 3, 4, 6$. The order parameters and correspondingresponse functions as well as the internal energy are calculated and examinedin detail in order to feature the real nature of phase boundaries andcorresponding temperatures. The thermal variations of the average magnetizationare classified according to the N\'{e}el nomenclature.

Bethe lattice approach study of the mixed spin-$\frac{1}{2}$ and spin-$\frac{7}{2}$ Ising model in a longitudinal magnetic field