  Persistant current in isolated mesoscopic rings is studied using the
continium and tight-binding models of independent electrons. The calculation is
performed with disorder and also at finite temperature. In the absence of
disorder and at zero temperature agreement is obtained with earlier results by
D. Loss et. al., in that there is half quantum flux periodicity for a large and
odd number of electrons, but full quantum periodicity for any even number of
electrons in the ring. Strong, disorder converts the period into full quantum
periodicity. Finite temperature reduces the magnitude of the current, but
preserves the quantum flux periodicity at zero temperature. However the sign of
the current may change as disorder or temperature is increased. A
generalization of the parity effect, previously discussed by Legett, Loss and
Kusmartsev is described for the case where there are electrons with spin,
influenced by finite temperature and disorder.

Condensed Matter