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We discuss theoretically the magnetically ordered phase induced by magneticand nonmagnetic impurities in three-dimensional and quasi-low-dimensionalsystems with singlet ground states separated by a gap from excited tripletstates. Using ideas of the percolation theory, we estimate the transitiontemperature $T_N(n)$ to the N\'eel phase at a small concentration $n$ ofdefects, derive the density of states of low-energy elementary excitations, andexamine the contribution of these excitations to the specific heat andmagnetization. Our expressions for $T_N(n)$ and for the specific heat describewell available experimental findings obtained in various appropriate systems:spin-$\frac12$ dimer materials, spin-ladder compounds, spin-Peierls and Haldanechain materials. However, our expression for $T_N(n)$ differs considerably frommany of those proposed before.

Critical temperature and low-energy excitations in gapped spin systems with defects