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Periodic striped configurations in the large volume limit
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Paper
Periodic striped configurations in the large volume limit
2021
Overview
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 \\(\\). For \\(<0\\) minimizers are trivial uniform states. It is conjectured that \\(\\,d2\\) there exists \\(0<1\\) such that for all \\(0<\\) and for all \\(L>0\\) minimizers are striped/lamellar patterns. In Daneri-Runa arXiv:1702.07334 the authors prove the above for \\(L=2kh^*_\\), where \\(kın\\) and \\(h^*_\\) is the optimal period of stripes for a given \\(0<\\). The purpose of this paper is to show the validity of the conjecture for generic \\(L\\).
Publisher
Cornell University Library, arXiv.org
Subject
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