Periodic striped states in Ising models with dipolar interactions

We review the problem of determining the ground states of two-dimensional Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling J is sufficiently large, the ground states are periodic and “striped”. More precisely, we prove a restricted version of the conjecture, by constructing the minimizers within the variational class of states whose domain walls are arbitrary collections of horizontal and/or vertical straight lines.