English

The BCC lattice in a long range interaction system

Analysis of PDEs 2022-08-02 v1

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 (Δ)3/2(-\Delta)^{-3/2}, it is proved that the body centered cubic lattice is the preferred structure.

Keywords

Cite

@article{arxiv.2208.00528,
  title  = {The BCC lattice in a long range interaction system},
  author = {Xiaofeng Ren and Juncheng Wei},
  journal= {arXiv preprint arXiv:2208.00528},
  year   = {2022}
}
R2 v1 2026-06-25T01:21:56.313Z