Scaling of I-V characteristics of Superconducting wire networks at irrational uniform frustration

Current-voltage characteristics of uniform Al wire networks with various values of frustration index f are found to be consistent with a transition to a fully superconducting (R=0) state. Scaling of these characteristics, usually indicative of a continuous transition, is found to occur at special irrational f values such as the inverse golden mean -1 but not at nearby low-order rationals. London-loop simulations for these cases suggest a self-similar ground state which is most likely never attained due to the presence of nearly degenerate disordered states such as those found in glasses.