Crystalline Order on a Sphere and the Generalized Thomson Problem

Details Crystalline Order on a Sphere and the Generalized Thomson Problem Crystalline Order on a Sphere and the Generalized Thomson Problem

2002-06-10

arxiv.org/abs/cond-mat/0206144v3

Phys.Rev.Lett.89:185502,2002

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixed

Scientific paper

10.1103/PhysRevLett.89.185502

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.

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