Slow relaxation in superconducting arrays

Relaxation behavior of two-dimensional superconducting arrays at low temperatures is investigated as the frustration due to transverse magnetic fields is varied. In the fully frustrated case, the relaxation is shown to be of a stretched exponential form, which is in sharp contrast with the algebraic one in the absence of magnetic fields. On the other hand, it is found that irrational frustration brings about peculiar size-dependence, manifesting the intrinsic finite-size effects present in the system. Finally, in the XY gauge glass, corresponding to the array under random magnetic fields, algebraic relaxation is observed, reflecting the emergence of algebraic glass ordering at low temperatures.