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Based on the Ising model, using the Monte Carlo method, we examine the magnetic and thermodynamic characteristics of a ferrimagnetic hexagonal nanowire with spin-5/2 and spin-7/2 of alternate layer structure under external and longitudinal crystal magnetic fields, in particular the physical effect of the external magnetic field on compensation behavior. Moreover, the phase diagrams in the ( T , D / J s ), ( T , J int / J s ), and ( T , J σ / J s) planes have been detailed. Consequently, we have obtained single and double compensation temperatures for the determined longitudinal crystal and external field parameters. The magnetizations of type-N, type-Q, and type-M have been found for certain parameter values in our system. This research was compared with other theoretical and experimental findings. [ABSTRACT FROM AUTHOR]