  We examine the spin asymmetry of ground states for two-dimensional,
harmonically trapped two-component gases of fermionic atoms at zero temperature
with weakly repulsive short range interactions. Our main result is that, in
contrast to the three-dimensional case, in two dimensions a non-trivial
spin-asymmetric phase can only be caused by shell structure. A simple,
qualitative description is given in terms of an approximate single particle
model, comparing well to the standard results of Hartree-Fock or direct
diagonalization methods.
