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The BCC lattice in a long range interaction system (2208.00528v1)
Published 31 Jul 2022 in math.AP
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.