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Infinite geometric frustration in a cubic dipole cluster

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Schönke,  Johannes
Max Planck Research Group Emerging Complexity in Physical Systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Schneider,  Tobias
Max Planck Research Group Emerging Complexity in Physical Systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Schönke, J., Schneider, T., & Rehberg, I. (2015). Infinite geometric frustration in a cubic dipole cluster. Physical Review B, 91(2): 020410(R). doi:10.1103/PhysRevB.91.020410.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002A-397D-B
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 eight interacting dipoles in a cubic cluster is investigated in detail. Instead of discrete equilibria we find a 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 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.