Three-dimensional Josephson-junction arrays:Static magnetic response

In this work we present a simple three-dimensional Josephson-junction array model: a cube with twelve junctions, one on each edge. The low-field magnetic response of the system is studied numerically for arbitrary directions of the applied field. In this model the magnetic energy of the circulating currents is taken into account by introducing an effective mutual inductance matrix. The lower threshold field for flux penetration is determined in a closed analytic form for field directions perpendicular to one cube side.