  A careful study on the mesoscopic PC in a Luttinger liquid ring is carried
out.
  It is shown that discreteness plays an important role in calculating the PC
caused by the magnetic flux. At zero temperature, the current is shown to be
independent of the interaction even when $g=g_2-g_4$ is not zero. The current
becomes enhanced at finite temperatures comparing to the non-interacting case,
when the parameter g is positive.
