The glassy state in arrays of superconducting junctions: the role of frustration and disorder in its formation

We have submitted to a close scrutiny the genesis of the glassy (or better the fully incommensurate) state in arrays of superconducting junctions at zero temperature. From our numerical simulations, using the XY hamiltonian, it comes out that frustration by itself is a necessary but not a sufficient condition. The other needed element is the disorder. However only the positional disorder is effective in the formation of a truly incommensurate state. The oscillation damping in the ground state energy and in the magnetic moment, as a function of the frustration, is not linear. The critical frustration (characteristic of the short range "order-disorder" crossover) decreases almost linearly with the root mean square of plaquette area, but not in a "universal" manner. © 1994.