Two-dimensional Ising model with competing interactions and its application to clusters and arrays of $\pi$-rings and adiabatic quantum computing

A. O'Hare, F. V. Kusmartsev, K. I. Kugel +1

We study planar clusters consisting of loops including a Josephson $\pi$-junction ($\pi$-rings). Each $\pi$-ring carries a persistent current and behaves as a classical orbital moment. T…