Quantum spin chains with regularly alternating bonds and fields

We consider the spin-1/2 XY chain in a transverse field with regularly varying exchange interactions and on-site fields. In two limiting cases of the isotropic XX and extremely anisotropic (Ising) exchange interaction the thermodynamic quantities are calculated rigorously with the help of continued fractions. We discuss peculiarities of the low-temperature magnetic properties and a possibility of the spin-Peierls instability.