  We investigate the effect of degenerate atomic states on the exciton
delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen
gas and regular one-, two-, and three-dimensional lattice arrangements as
examples, we see that degeneracies can enhance the delocalization compared to
the situation when there is no degeneracy. Using the Zeeman splitting provided
by a magnetic field, we controllably lift the degeneracy to study in detail the
transition between degenerate and non-degenerate regimes.
