Correlations and Disorder in Arrays of Magnetically Coupled Superconducting Rings

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Abstract
We have used ultrasensitive susceptibility techniques and scanning Hall probe microscopy to study arrays of electrically isolated micron-sized superconducting rings. The magnetic moments produced by the supercurrents in these rings are analogous to Ising spins, and neighboring rings interact antiferromagnetically via their dipolar magnetic fields. We find that there are significant antiferromagnetic correlations between rings, and effects due to geometrical frustration can be observed. Quenched disorder also plays a significant role, suppressing the development of true long-range order.