  Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain
with nearest neighbor interaction in a uniform transverse field is studied
based on the simple exact solutions. It is found that there are [N/2]
level-crossing points in the ground state, where N is the periodic number of
the system and [x] stands for the integer part of x, when the interaction
strength and magnitude of the magnetic field satisfy certain conditions. The
quantum phase transitions are of the first order due to the level-crossing. The
ground state in the thermodynamic limit will be divided into three
distinguishable quantum phases.
