05-05E

Using the Jordan--Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin--$\frac {1}{2}$ transverse Ising chain with periodically varying intersite interactions or/and on--site fields. We consider in detail chains having periods of modulation 2 and 3. We compare the thermodynamic properties of regularly alternating transverse Ising and transverse $XX$ chains. Moreover, we compare the ground--state properties of regularly alternating quantum and classical chains. Making use of the corresponding unitary transformations we extend the elaborated approach for a study of thermodynamics of regularly alternating spin--$\frac {1}{2}$ anisotropic $XY$ chains without field. We use the exact expression for the ground--state energy of such a chain of period 2 to discuss how the exchange interaction anisotropy destroys the spin--Peierls dimerized phase.