  Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by
combining the decoration-iteration transformation with the method of exact
recursion relations. Exact results for critical lines, compensation
temperatures, total and sublattice magnetizations are obtained from a precise
mapping relationship with the corresponding spin-1/2 Ising model on a simple
(undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction
and single-ion anisotropy on magnetic properties of the ferrimagnetic model is
investigated in particular. It is shown that the total magnetization may
exhibit multicompensation phenomenon and the critical temperature vs. the
single-ion anisotropy dependence basically changes with the coordination number
of the underlying Bethe lattice. The possibility of observing reentrant phase
transitions is related to a high enough coordination number of the underlying
Bethe lattice.
