Period and amplitude halving in mesoscopic rings with spin

We consider the flux dependence of persistent currents in mesoscopic rings threaded by magnetic flux, and extend well-known arguments to include particles of spin 1/2. We find several interesting consequences of spin, such as period and amplitude halving in a single ring, without including electron-electron interactions, transverse channels, or disorder. These consequences depend sensitively on the fixed number (modulo 4) of particles on a given ring, and lead to strong fluctuations between samples containing a small number of rings.