  This paper describes a study on fractional flux periodicity of the ground
state in planar systems made from a square lattice whose boundary is compacted
into a torus. It is pointed out that, in the long length and large diameter
limit of a torus, the ground-state energy and persistent currents show a
fractional period of the fundamental unit of magnetic flux depending on the
twist around the torus axis. We discuss the possible relationship between the
twist and genus of a torus, and comment on fractional flux periodicity in a
cylinder.

Mesoscale and Nanoscale Physics;Superconductivity;High Energy Physics - Theory