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 $T_c$ superconductors with annealed disorder is presented.