Glassy phase in an array of Josephson junctions

We study the critical behavior of an irrationally frustrated XY model on a square lattice as a model for the Josephson-junction array in an incommensurate magnetic field. Approximate arguments are presented suggesting that the system will exhibit successive orderings at larger and larger length scales with fewer and fewer defects as the temperature is lowered. This low-temperature phase appears to display features very similar to those in the replica-symmetry-breaking formulation of spin glasses, which strongly suggest a glassy phase without any disorder. We propose a Parisi-like order parameter for this state.