  The exact solutions for the energy spectrum of the XX model with a periodic
coupling and an external transverse magnetic field $h$ are obtained. The
diagonalization procedure is discussed, and analytical and numerical solutions
are given. Using the solutions for period-two coupling, the free energy,
entropy, and specific heat are calculated as functions of temperature and
applied transverse external magnetic field. Their expressions show that below a
particular value $v$ and above a value $u$ of the magnetic field $|h|$, the
entropy and the specific heat vanish exponentially in the low temperature
limit.
