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arXiv · 2405.06542

Microstructures and anti-phase boundaries in long-range lattice systems

Andrea Braides·Edoardo Voglino·Matteo Zanardini
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Abstract

We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex. If short-range interactions are non-convex we then have a competition between short-range oscillations and long-range ordering. In the case of a double-well nearest-neighbour potential, thanks to a recent result by Braides, Causin, Solci and Truskinovsky, we are able to show that such a competition generates $M$-periodic minimizers whose arrangements are driven by an interfacial energy. Given $M$, the shape of such minimizers is universal, and independent of the details of the energies, but the number and shapes of such minimizers increases as $M$ diverges.

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Andrea Braides, Edoardo Voglino, Matteo Zanardini. 2024-05-10. Microstructures and anti-phase boundaries in long-range lattice systems. https://arxiv.org/abs/2405.06542

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