Abstract
The ground state of a two-dimensional square superconducting π ring array has been investigated. The circulating currents of the π 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 π ring's inductance parameter β = 2πLIc/φ0. For a small β 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 φ0/4 in each ring. Moreover, the magnetic field needed to destroy the anti-parallel configuration will be very small when β is large enough.