Thermodynamic properties of the periodic nonuniform spin- isotropic XY chains in a transverse field

Using the Jordan–Wigner transformation and the continued-fraction method we calculate exactly the density of states and thermodynamic quantities of the periodic nonuniform spin- isotropic XY chain in a transverse field. We discuss in detail the changes in the behaviour of the thermodynamic quantities caused by regular nonuniformity. The exact consideration of thermodynamics is extended including a random Lorentzian transverse field. The presented results are used to study the Peierls instability in a quantum spin chain. In particular, we examine the influence of a nonrandom/random field on the spin-Peierls instability with respect to dimerization.