Border effects on the ground state of an ultrathin magnetic film model

In the study of ultrathin magnetic films, one of the most simple and widely studied model is the two-dimensional Ising model with short-range ferromagnetic exchange and long-range antiferromagnetic dipolar interactions (ILRA model). In substrates with periodic boundary conditions, it is well known that the ground state of this system, depending on the strength parameter $$\delta $$ δ , is given by the antiferromagnetic, the irregular checkerboard and the striped states. In this work, we study the border effects on the ground state. We develop a systematic study on square substrates of size $$L\times L$$ L × L with open boundary conditions focusing our attention on the range $$0.35\leqslant \delta \leqslant 0.75$$ 0.35 ⩽ δ ⩽ 0.75 . Our results show that, at intermediate values of $$\delta $$ δ , none of the configurations present on substrates with periodic boundary conditions correspond to the ground state of the system. Specifically, we find three new kinds of ground states for $$ L \le 8 $$ L ≤ 8 , which are also our best candidates to be ground state in systems of sizes up to $$ L = 100$$ L = 100 . Also, by means of the same systematic study on a similar short-range model, we analyze which of these ground states is a consequence of the long-range character of the dipolar interactions in the ILRA model. Graphical Abstract Ground states for $$8 \times 8$$ 8 × 8 lattice in the range of the strength parameter $$0.35\leqslant \delta \leqslant 0.75$$ 0.35 ⩽ δ ⩽ 0.75