Spontaneous magnetization in superconducting pi ring and 0 ring mixed arrays

Regular mixed arrays of superconducting pi rings and 0 rings have been investigated. Our calculation shows that the free energy of inverse spontaneous magnetization of two pi rings indirectly coupled via a 0 ring is lower. The state of the full antiparallel pattern of pi rings is favorable in the regular mixed arrays. This is a quantum phase coherence result of superconducting wave functions.