  We study pattern formation within the $J_1$-$J_3$ - spin model on a
two-dimensional square lattice in the case of incompatible (ferromagnetic)
boundary conditions on the spin field. We derive the discrete-to-continuum
$\Gamma$-limit at the helimagnetic/ferromagnetic transition point, which turns
out to be characterized by a singularly perturbed multiwell energy functional
on gradient fields. Furthermore, we study the scaling law of the discrete
minimal energy. The constructions used in the upper bound include besides
rather uniform or complex branching-type patterns also structures with
vortices. Our results show in particular that in certain parameter regimes the
formation of vortices is energetically favorable.
