We calculate the current-voltage $\mathrm{}\left(\mathrm{IV}\right)\mathrm{}$ characteristics of a Josephson-junction array with long-range interactions. The array consists of two sets of equally spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wires cross. We treat each such junction as an overdamped resistively shunted junction, and each wire segment between two junctions as a similar resistively shunted junction with a much higher critical current. The $\mathrm{IV}$ characteristics are obtained by solving the coupled Josephson equations numerically. We find that, for a sufficiently large number of wires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculated $\mathrm{IV}$ characteristics also show a striking hysteresis, even though each of the individual junctions is nonhysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower voltage branches, and is also in excellent agreement with experiment.

• Received 20 May 1997

DOI:https://doi.org/10.1103/PhysRevB.56.8335