An effective free energy was proposed for the physics of disclination defects in particle arrays which were constrained to move on an arbitrary 2-dimensional surface. For finite temperatures, the physics of interacting disclinations were mapped onto a Laplacian sine-Gordon Hamiltonian which was suitable for numerical simulations. General features of the ground state were identified and then transferred to the spherical case. The ground state was analyzed as a function of the ratio of the defect core energy to the Young’s modulus. It was argued that the core energy contribution became less and less important in the limit where the radius of the sphere was much greater than the particle spacing. For large core energies, there were 12 disclinations which formed an icosahedron. At intermediate core energies, unusual finite-length grain boundaries were preferred. A complicated regime of small core energies, in the limit where the above radius/spacing ratio approached infinity, was also considered. The method was applied to the classic (Thomson) problem of finding the ground-state of electrons distributed on a 2-sphere.

Interacting Topological Defects on Frozen Topographies. M.J.Bowick, D.R.Nelson, A.Travesset: Physical Review B, 2000, 62[13], 8738-51