  Phase transitions, compensation phenomenon and magnetization of a
ferro-ferrimagnetic ternary alloy AB$_{\rho}$C$_{1-\rho}$ composed of three
different kinds of magnetic ions A, B and C with the spin magnitude 1/2, 1 and
3/2 are examined within the framework of a mixed-spin Ising model on a
honeycomb lattice with a selective annealed site disorder on one of its two
sublattices. It is supposed that the first sublattice of a bipartite honeycomb
lattice is formed by the spin-1/2 magnetic ions, while the sites of the second
sublattice are randomly occupied either by the spin-1 magnetic ions with a
probability $\rho$ or the spin-3/2 magnetic ions with a probability $1-\rho$,
both being subject to a uniaxial single-ion anisotropy. The model under
investigation can be exactly mapped into an effective spin-1/2 Ising model on a
triangular lattice through the generalized star-triangle transformation. For a
specific concentration of the spin-1 (spin-3/2) magnetic ions, it is shown that
the ferro-ferrimagnetic version of the studied model may display a compensation
temperature at which the total magnetization vanishes below a critical
temperature. The critical temperature strikingly may also become independent of
the concentration of the randomly mixed spin-1 and spin-3/2 magnetic ions for a
specific value of a uniaxial single-ion anisotropy. The spontaneous magnetic
order may be notably restored at finite temperatures through the
order-by-disorder mechanism above a disordered ground state, which results in
an anomalous temperature dependence of the total magnetization with double
reentrant phase transitions.
