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 [Formula presented] of the underlying lattice and the core energy [Formula presented] 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 [Formula presented] ([Formula presented]) 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)