Orientational ordering of point dipoles on a sphere

Gnidovec, Andraž; Čopar, Simon

doi:10.1103/physrevb.102.075416

Cited by 8 publications

(8 citation statements)

References 36 publications

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“…ref. 56), but it is expected as dipolar configurations are not geometrically frustrated on locally triangular lattices. Nevertheless, we find that many individual configurations with symmetric quadrupolar order are possible on certain lattices with high positional order symmetry, not only in the ground state but also in the excited state configurations.…”

Section: Resultsmentioning

confidence: 99%

“…ref. 56). In quadrupolar systems on a sphere, it leads to strong geometric frustration, especially considering the topological requirement for lattice defects which act as local points of frustration.…”

Section: Resultsmentioning

confidence: 99%

“…[53][54][55] Furthermore, orientational ordering in systems with pure multipolar interaction, specifically the dipole-dipole interaction, has also recently been studied on spherical lattices. 56,57 It was shown that the local positional order and the symmetry of the lattice play a fundamental role in determining the symmetries of the ground state and excited state configurations.…”

Section: Introductionmentioning

confidence: 99%

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Long-range order in quadrupolar systems on spherical surfaces

Gnidovec

Čopar

2021

Soft Matter

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Long-range order in quadrupolar systems on spherical surfaces

Gnidovec

Čopar

2021

Soft Matter

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“…Intriguing structural order supported by curvature and interaction anisotropy emerges in liquid crystals [30,31], dynamical systems [32,33] and thin magnetic spherical shells [34][35][36]. Furthermore, orientational ordering in systems with pure multipolar interaction, specifically the dipole-dipole interaction, has also recently been studied on spherical lattices [37,38]. It was shown that the local positional order and the symmetry of the lattice play a fundamental role in determining the symmetries of the ground state and excited state configurations.…”

Section: Introductionmentioning

confidence: 99%

Long-range order in quadrupolar systems on spherical surfaces

Gnidovec¹,

Čopar²

2021

Preprint

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Understanding the interplay between topology and ordering in systems on curved manifolds, governed by anisotropic interactions, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.

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“…As a model, we consider N charges on a unit sphere that is a platform in the Thomson problem and/or the Smale's seventh problem [6]: to determine the minimum energy configuration of N charges confined to the surface of a unit sphere. The global and local minima of the PES have been investigated for this system [7][8][9][10][11][12], while many related problems have also been studied [13][14][15][16][17]. Through the total energy calculations for N ≤ 200, N = 12, 32, 72, 122, 132, 137, 146, 182, 187, and 192 have been identified to be magic numbers [7].…”

Section: Introductionmentioning

confidence: 99%

Magic numbers for vibrational frequency of charged particles on a sphere

Ono

2021

Preprint

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Finding minimum energy distribution of N charges on a sphere has been known as the Thomson problem. Here, we study the vibrational properties of the N charges in the lowest energy state within the harmonic approximation for 10 ≤ N ≤ 200 and for selected sizes up to N = 372. The maximum frequency ωmax increases with N 3/4 , which is rationalized by studying the lattice dynamics of two-dimensional triangular lattice. The N -dependence of ωmax identifies magic numbers of N = 12, 32, 72, 132, 192, 212, 272, 282, and 372, reflecting both a strong degeneracy of one-particle energies and an icosahedral structure that the N charges form. N = 122 is not identified as a magic number for ωmax because the former condition is not satisfied.

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Orientational ordering of point dipoles on a sphere

Cited by 8 publications

References 36 publications

Long-range order in quadrupolar systems on spherical surfaces

Long-range order in quadrupolar systems on spherical surfaces

Long-range order in quadrupolar systems on spherical surfaces

Magic numbers for vibrational frequency of charged particles on a sphere

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