  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.
