We review some recent results on statistical mechanics of the one-dimensional spin-1/2 XY systems paying special attention to the dynamic and thermodynamic properties of the models with Dzyaloshinskii-Moriya interaction, correlated disorder, and regularly alternating Hamiltonian parameters.
We extend the consideration of the spin-21 transverse XY chain with correlated Lorentzian disorder [Phys. Rev. B 55, 14 298 (1997)] for the case of additional Dzyaloshinskii-Moriya interspin interaction. It is shown how the averaged density of states can be calculated exactly. Results are presented for the density of states and the transverse magnetization.