The annealed positions of ferromagnetic bonds doped into a 2D antiferromagnet

We determine where a given concentration of ferromagnetic (FM) bonds doped into a square lattice antiferromagnet must go to minimize the system's total magnetic energy. We find i) an infinite degeneracy of ground-state arrangements of FM bonds that correspond to completely unfrustrated configurations for classical spins, and ii) this degeneracy is lifted when quantum fluctuations are included, and phase-separated ground states, such as periodic arrays of stripes of FM bonds, are found. A discussion of the application of these ideas to doped cuprate high-Tc superconductors with annealed disorder is presented.