Shape anisotropy and magnetic domain structures in striped monolayers

We study the effect of dipolar interactions on a magnetic striped monolayer with a microscopic unit cell of square symmetry, and of size $(N_x\times N_y)$ spins. Even if the aspect ratio $r=N_x/N_y$ is very large, an in-plane shape anisotropy is always negligible, except if $N_y$ is fairly small $(N_y<40)$. In-plane domains are not possible, except for values of the dipolar coupling larger than the domain wall energy.