  By solving the Rashba model of mesoscopic rings, we give analytically the
ground-state properties of the ring, including the spin polarization, the
persistent charge and spin currents (PCC and PSC). These ground-state
properties can be given based on four kinds of electron numbers in rings. The
effect of the self-inductance of the ring leads to the self-sustained magnetic
flux (SSMF) and the self-sustained PCC and PSC, which break spontaneously
time-reversal symmetry to form orbital magnetic phase (OMP). To tune the
spin-orbit coupling strength or electron number of the ring can induce the
phase transition between the OMP and non-OMP. For exact one-dimensional rings
we find the coexistence of the pure PSC and SSMF. This property of the pure PSC
may provide a new scheme to measure the pure PSC.
