Commensurate states in disordered networks

We have measured the phase boundary ${\mathit{T}}_{\mathit{c}}$(H) for a series of superconducting wire networks with different types and degrees of disorder. The basic pattern to be perturbed was the square net. In the first series lines were randomly displaced from their periodic positions (preserving the long-range order), and in the second series their spacing was randomly varied about an average (destroying the long-range periodic order). These studies on these systems are similar to studies on Josephson-junction arrays with correlated random areas. In the last series the two-dimensional periodicity was destroyed by randomly displacing successive rows of squares while leaving the areas unchanged; the result is a network with quasi-one-dimensional periodic order. The effects of the areal disorder are dramatic and lead to the decay of structure on the phase boundary regardless of whether or not long-range order has been destroyed. The destruction of long-range order in one direction, however, leaves the phase boundary virtually unchanged. The data are compared with previous theoretical treatments and are analyzed using the ‘‘${\mathit{J}}^2$’’ model, in which one considers only the kinetic energy of the induced currents resulting from fluxoid quantization. This model explains most of the features of the experimental data and yields quantitative predictions for some.