Investigation of spontaneous magnetization of coupled 2×2 superconducting \pi ring array

We present the theoretical investigation of spontaneous magnetization of a coupled 2×2 \pi ring array. It is indicated by free energy calculation that the system has the lowest energy when the four \pi rings have the full antiparallel configuration. Furthermore, the numerical evaluation results show that the system which favours full antiparallel spontaneous magnetization is a quantum effect deriving from the phase cohering of the superconducting quantum wavefunctions in the four superconducting rings through the shared Josephson junctions.