  A cylindrical magnetic nanowire system composed of ferromagnetic core and
shell layers has been investigated by using effective field theory with
correlations. Both ferromagnetic and antiferromagnetic exchange couplings at
the core-shell interface have been considered. Main attention has been focused
on the effects of the quenched disordered shell bonds, as well as interface
bonds on the magnetic properties of the system. A complete picture of the phase
diagrams and magnetization profiles has been represented. It has been shown
that for the antiferromagnetic nanowire system, the magnetization curves can be
classified according to N\'{e}el theory of ferrimagnetism and it has been found
that under certain conditions, the magnetization profiles may exhibit Q-type,
P-type, N-type and L-type behaviors. The observed L-type behavior has not been
reported in the literature before for the equilibrium properties of nanoscaled
magnets. As another interesting feature of the system, it has been found that a
compensation point can be induced by a bond dilution process in the surface.
Furthermore, we have not found any evidence of neither the first order phase
transition characteristics, nor the reentrance phenomena.
