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

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.