Crystalline Order on a Sphere and the Generalized Thomson Problem

M. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset
Phys. Rev. Lett. 89, 185502 – Published 10 October 2002; Erratum Phys. Rev. Lett. 89, 249902 (2002)

Abstract

We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy Ecore of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/rγ (0<γ<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.

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  • Received 11 June 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.185502

©2002 American Physical Society

Erratum

Erratum: Crystalline Order on a Sphere and the Generalized Thomson Problem [Phys. Rev. Lett.PRLTAO0031-9007 89, 185502 (2002)]

M. Bowick, A. Cacciuto, D. R. Nelson, and A. Travesset
Phys. Rev. Lett. 89, 249902 (2002)

Authors & Affiliations

M. Bowick1, A. Cacciuto1, D. R. Nelson2, and A. Travesset3

  • 1Physics Department, Syracuse University, Syracuse, New York 13244-1130
  • 2Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138
  • 3Loomis Laboratory, University of Illinois at Urbana, Urbana, Ilinois 61801

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Issue

Vol. 89, Iss. 18 — 28 October 2002

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