Static properties of classical Josephson junction arrays: models and experimental achievements

This review deals with the static properties of classical Josephson arrays. We first comment on the model describing the system, both in the phase representation-the frustrated XY model-and in the vortex representation-the Coulomb gas model. Self-induced magnetic fields and disorder are added so as to faithfully reproduce physical systems. A review of scaling theory concerning the I-V curve-which provides relevant information about, for example, the proximity of a phase transition-is given in order to compare theoretical predictions with experimental results. Josephson arrays are characterized by an extremely rich phase diagram as a function of both external parameters (temperature, applied magnetic field) and inherent ones (disorder, self-inductance), Such a diagram is explored in the light of recent results. Questions such as those of the nature of the ground state and the stability of the static states, and the existence of a disordered vortex state due to disorder intrinsic to the array and/or to external influences arise.