  We discuss theoretically the magnetically ordered phase induced by magnetic
and nonmagnetic impurities in three-dimensional and quasi-low-dimensional
systems with singlet ground states separated by a gap from excited triplet
states. Using ideas of the percolation theory, we estimate the transition
temperature $T_N(n)$ to the N\'eel phase at a small concentration $n$ of
defects, derive the density of states of low-energy elementary excitations, and
examine the contribution of these excitations to the specific heat and
magnetization. Our expressions for $T_N(n)$ and for the specific heat describe
well available experimental findings obtained in various appropriate systems:
spin-$\frac12$ dimer materials, spin-ladder compounds, spin-Peierls and Haldane
chain materials. However, our expression for $T_N(n)$ differs considerably from
many of those proposed before.
