FrustratedXYmodel with screening

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Abstract
We consider a Josephson- or proximity-coupled superconducting array with finite geometrical inductance. The finite self-inductance is shown to screen the vortex-antivortex interaction in the arrays, converting the logarithmic interaction into a 1/r interaction at large separations in analogy with the effects of screening found by Pearl for a homogeneous superconducting film. We explicitly calculate the screening length in terms of the geometrical inductance and the intergrain Josephson-coupling strength. For typical arrays, the screening length is found to be of order 10 cm, independent of the plaquette dimensions of the array, although the length can be made smaller for strong couplings. An analogous type of screening is shown to occur in the cooperative-ring-exchange model of the fractional quantum Hall effect. In this latter case, the screening arises from the vibrations of the two-dimensional Wigner lattice in the presence of a strong magnetic field, producing fluctuations in the flux per lattice plaquette. The screening in this case also produces 1/r interactions between the elementary excitations of the system. However, the screening is very slow, and hence only effective at very long times.