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We show striped pattern formation in the large volume limit for a class ofgeneralized antiferromagnetic local/nonlocal interaction functionals in generaldimension previously considered Goldman-Runa and Daneri-Runa and inGiuliani-Lieb-Lebowitz and Giuliani-Seiringer in the discrete setting. In sucha model the relative strength between the short range attractive term favouringpure phases and the long range repulsive term favouring oscillations ismodulated by a parameter $\tau$. For $\tau<0$ minimizers are trivial uniformstates. It is conjectured that $\forall\,d\geq2$ there exists$0<\bar{\tau}\ll1$ such that for all $0<\tau\leq\bar{\tau}$ and for all $L>0$minimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 theauthors prove the above for $L=2kh^*_\tau$, where $k\in\N$ and $h^*_\tau$ isthe optimal period of stripes for a given $0<\tau\leq\bar{\tau}$. The purposeof this paper is to show the validity of the conjecture for generic $L$.

Periodic striped configurations in the large volume limit