In this talk, singularly perturbed energies arising from discrete J1-J3-models are studied. The energies under consideration consist of a non-convex bulk term and a higher-order regularizing term, and are subject to incompatible boundary conditions. In contrast to existing results in the literature, admissible fields are in this talk not necessarily gradients. Instead, their curl is linked to topological singularities in the discrete J1-J3-model. We present a scaling law for the minimal energy in terms of three parameters: one measuring the incompatibility of the boundary conditions, the second measuring the strength of the regularizing term, and the third being related to the interatomic distance in the discrete model. This result implies in particular that in certain parameter regimes minimizers necessarily develop vortices. A key tool in the analysis is a careful modification of the ball-construction technique, in which - due to a lack of rigidity - the bulk energy and the higher-order regularizing term need to be considered simultaneously.