Mjw. Dodgson, INVESTIGATION ON THE GROUND-STATES OF A MODEL THIN-FILM SUPERCONDUCTOR ON A SPHERE, Journal of physics. A, mathematical and general, 29(10), 1996, pp. 2499-2508
We consider the problem of finding the ground state of a model type-II
superconductor on the two-dimensional surface of a sphere, penetrated
by N vortices. Numerical work shows the ground states to consist of a
triangular network of the vortices with twelve five-coordinated centr
es. Values of N are found with particularly low-energy ground states,
due to structures of high symmetry. The large-N limit is treated withi
n elasticity theory to compare with the triangular vortex lattice that
forms the ground state on an infinite flat plane. Together with numer
ical work this demonstrates that the thermodynamic limit N --> infinit
y of the spherical system remains different from the fat plane due to
the presence of twelve disclination defects.