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arXiv · 2208.00528

The BCC lattice in a long range interaction system

Xiaofeng Ren·Juncheng Wei
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Abstract

While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short range interaction energy and a long range interaction energy. In three dimensions, and when the long range interaction is given by the nonlocal operator $(-\Delta)^{-3/2}$, it is proved that the body centered cubic lattice is the preferred structure.

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Xiaofeng Ren, Juncheng Wei. 2022-07-31. The BCC lattice in a long range interaction system. https://arxiv.org/abs/2208.00528

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