Ground state of the uniformly frustrated two-dimensional XY model near f=1/2

Teitel and Jayaprakash have conjectured that the ground states for the uniformly frustrated XY model (a model for the Josephson network in a magnetic field) are periodic on a q×q cell when the frustration factor f (the magnetic flux measured in units of the flux quantum) is a rational number p/q. We have found examples for f close to 1/2 where a larger cell<apparently 2q×2q<is required. We conjecture that something similar occurs whenever f is sufficiently close to a simple ratio.