Periodic striped configurations in the large volume limit

Sara Daneri; Eris Runa

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arXiv · 2110.09914

Periodic striped configurations in the large volume limit

Sara Daneri·Eris Runa

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Abstract

We show striped pattern formation in the large volume limit for a class of generalized antiferromagnetic local/nonlocal interaction functionals in general dimension previously considered Goldman-Runa and Daneri-Runa and in Giuliani-Lieb-Lebowitz and Giuliani-Seiringer in the discrete setting. In such a model the relative strength between the short range attractive term favouring pure phases and the long range repulsive term favouring oscillations is modulated by a parameter $τ$. For $τ<0$ minimizers are trivial uniform states. It is conjectured that $\forall\,d\geq2$ there exists $0<\barτ\ll1$ such that for all $0<τ\leq\barτ$ and for all $L>0$ minimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 the authors prove the above for $L=2kh^*_τ$, where $k\in\N$ and $h^*_τ$ is the optimal period of stripes for a given $0<τ\leq\barτ$. The purpose of this paper is to show the validity of the conjecture for generic $L$.

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Sara Daneri, Eris Runa. 2021-10-19. Periodic striped configurations in the large volume limit. https://arxiv.org/abs/2110.09914

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