  We consider Ising models in two and three dimensions with nearest neighbor
ferromagnetic interactions and long range, power law decaying,
antiferromagnetic interactions. If the strength of the ferromagnetic coupling J
is larger than a critical value J_c, then the ground state is homogeneous and
ferromagnetic. As the critical value is approached from smaller values of J, it
is believed that the ground state consists of a periodic array of stripes (d=2)
or slabs (d=3), all of the same size and alternating magnetization. Here we
prove rigorously that the ground state energy per site converges to that of the
optimal periodic striped/slabbed state, in the limit that J tends to the
ferromagnetic transition point. While this theorem does not prove rigorously
that the ground state is precisely striped/slabbed, it does prove that in any
suitably large box the ground state is striped/slabbed with high probability.
