Ground state of a superconducting pi ring array under external magnetic fields

The ground state of a two-dimensional square superconducting pi ring array has been investigated. The circulating currents of the pi ring array will spontaneously magnetize to the 'antiferromagnetic' arrangement with directions of the nearest-neighbouring currents circulating oppositely in the absence of an external magnetic field. It is found that the external magnetic field could destroy the anti-parallel configuration effectively. The external magnetic field needed to destroy the anti-parallel configuration is related to the superconducting pi ring's inductance parameter beta = 2 pi LIc/phi(0). For a small beta the anti-parallel configuration, which is the lowest-energy ground state of the system, will be fully destroyed and changed to the configuration that the circulating currents have the same direction and parallel to the external magnetic field when the magnetic flux reaches phi(0)/4 in each ring. Moreover, the magnetic field needed to destroy the anti-parallel configuration will be very small when beta is large enough.