Infinite Geometric Frustration in a Cubic Dipole Cluster
Abstract
The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of 8 interacting dipoles in a cubic cluster is investigated in detail. Instead of discrete equilibria we find a new type of ground state consisting of infinitely many orientations. This continuum of energetically degenerate states represents a yet unknown form of magnetic frustration. The corresponding dipole rotations in the flat potential valley of this Goldstone mode enable the construction of frictionless magnetic couplings. Using novel computer-assisted algebraic geometry methods, we moreover completely enumerate all equilibrium configurations. The seemingly simple cubic system allows for exactly 9536 unstable discrete equilibria falling into 183 distinct energy families.
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Cite
@article{arxiv.1408.4412,
title = {Infinite Geometric Frustration in a Cubic Dipole Cluster},
author = {Johannes Schönke and Tobias M. Schneider and Ingo Rehberg},
journal= {arXiv preprint arXiv:1408.4412},
year = {2015}
}
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5 pages