Current-voltage characteristics of uniform Al wire networks with various values of frustration index / 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 / values such as the inverse golden mean T -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. PACS numbers: 74.90.+n, 74.40.+k, 75.10.Nr Periodic superconducting wire networks [1] and Josephson junction arrays [2] are excellent systems for studying the effects of uniform frustration since its value can be precisely tuned by the application of a magnetic field. They are the closest experimental realizations of the uniformly frustrated 2D XY model which has been extensively studied [3-5]. Unlike the cases of spinglasses [6], high-7Y superconductors [7], and other frustrated systems with quenched disorder, as yet no experimental evidence for a thermodynamic glass transition has been found in a system without randomness. In superconducting arrays the frustration arises from the interplay between the lattice periodicity and the flux lattice periodicity. The resulting complex structure of the ground-state energy as a function of frustration [8], indexed by / ^O/Oo, where 0= Ha 1 is the average flux per cell and ^^h/le is the flux quantum, manifests itself experimentally as sharp maxima in the mean-field transition temperature, 7V, at low-order rational values of / [1,2]. The transitions to fully superconducting (/?=0) phases and the nature of those phases are partially understood for only the simplest cases [1-5]. There is general agreement that a Kosterlitz-Thouless (KT) transition occurs at /=0. Some evidence was found for a KT transition at/* 88 j [2], but theory suggests the involvement of an Ising transition [3]. Simulations have been interpreted as evidence of a first-order transition at /•• j [4].The question of what happens generally, i.e., at irrational / has been controversial. Halsey's [5] simulations showed that for irrational / such as the inverse of the golden mean T "' [r = (V5+1 )/2], the zero-temperature critical current / r (0) is not zero as had been originally proposed [3] and disordered vortex patterns were found. But his suggestion that a glass transition occurs at T > 0 for irrational /has not been generally accepted. A subsequent null result in a search for such a transition in Josephson junction arrays [9] confirmed the general belief, "that there can be no physical effect stemming from the irrationality of some parameter," since it would have "the property of being everywhere discontinuous" [8]. Scaling of the current-voltage (7-K) characteristics [7], argued to be the signature of a "vortex glass" transition in 3D-disordered superconductors [10], has thus far not been pursued in uniform 2D networks...

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