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Long-range order in quadrupolar systems on spherical surfaces.

AndraŽ Gnidovec1, Simon Čopar1

  • 1University of Ljubljana, Faculty of Mathematics and Physics, SI-1000 Ljubljana, Slovenia. andraz.gnidovec@fmf.uni-lj.si.

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Summary
This summary is machine-generated.

Geometric frustration on spherical lattices limits ordering of point quadrupoles. Caspar-Klug lattices offer diverse ground states, and substrate interactions can tune symmetry.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Curvature, confinement, and anisotropic interactions are key in curved manifold systems.
  • Understanding ordering phenomena in physical systems is crucial for various scientific fields.

Purpose of the Study:

  • Investigate how lattice symmetry and local order affect orientational ordering of point quadrupoles on a sphere.
  • Explore ground state configurations in systems with long-range interactions at zero temperature.

Main Methods:

  • Simulations of point quadrupoles on spherical lattices (triangular and Caspar-Klug).
  • Analysis of orientational ordering and ground state symmetries.
  • Modeling substrate interactions by constraining quadrupole tilts.

Main Results:

  • Locally triangular spherical lattices exhibit long-range order only in specific symmetric configurations due to geometric frustration.
  • Caspar-Klug lattices display diverse ground states with varying symmetries based on quadrupole positions.
  • Constraining quadrupole tilts and considering general tensors allow manipulation of ground state symmetry.

Conclusions:

  • Lattice symmetry and geometric frustration significantly impact quadrupolar ordering on spheres.
  • Caspar-Klug lattices provide a versatile platform for studying diverse ordered states.
  • Surface interactions offer a mechanism to control the symmetry of ground state configurations.