Abstract
We present an analytical investigation on the spontaneous magnetizationof infinitely large two-dimensional identical hexagonal superconductingπ-ring arrays based on an ansatz that each of theπ-rings carries a magnetic flux with the same frustration index. The free energies per ring,Un, in various states characterized by the number of zero-current (‘quiet’) junctionsn in the ring are calculated. A ladder relation of the energies has been demonstrated as, which basically shows that the fewer the quiet junctions of a state, the morefavourable the energy for the state formation. This result is in qualitativeagreement with the recent experimental observations in the large-scale hexagonalπ-loop (triangular half flux quantum) array (Hilgenkamp et al 2003 Nature 422 50–3).
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