Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-11-23
Phys. Rev. B62 (2000) 8738
Physics
Condensed Matter
Statistical Mechanics
36 pages, LaTeX, 30 color eps figures (also available on request)
Scientific paper
10.1103/PhysRevB.62.8738
We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature the physics of interacting disclinations is mapped to a Laplacian Sine-Gordon Hamiltonian suitable for numerical simulations. We then specialize to the case of a spherical crystal at zero temperature. The ground state is analyzed as a function of the ratio of the defect core energy to the Young's modulus. We argue that the core energy contribution becomes less and less important in the limit R >> a, where R is the radius of the sphere and a is the particle spacing. For large core energies there are twelve disclinations forming an icosahedron. For intermediate core energies unusual finite-length grain boundaries are preferred. The complicated regime of small core energies, appropriate to the limit R/a goes to infinity, is also addressed. Finally we discuss the application of our results to the classic Thomson problem of finding the ground state of electrons distributed on a two-sphere.
Bowick Mark J.
Nelson David R.
Travesset Alex
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