Fractional periodicity and magnetism of extended quantum rings

The magnetic properties and nature of the persistent current in small flux-penetrated $t-t'-U$ rings are investigated. An effective rigid-rotator description is formulated for this system, which coincides with a transition to a ferromagnetic state in the model. The criteria for the onset of effective rigid rotation is given. The model is used to understand continuum model ground-state solutions for a 2D few-particle hard-wall quantum dot, where ferromagnetic solutions are found even without the Zeeman coupling to spin. After the onset of effective rigid rotation, a 97--98% correspondence can be determined between the lattice model and continuum model eigenstate results.