  One of the challenges for fermionic cold atom experiments in optical lattices
is to cool the systems to low enough temperature that they can form quantum
degenerate ordered phases. In particular, there has been significant work in
trying to find the antiferromagnetic phase transition of the Hubbard model in
three dimensions, without success. Here, we attack this problem from a
different angle by enhancing the ordering temperature via an increase in the
degeneracy of the atomic species trapped in the optical lattice. In addition to
developing the general theory, we also discuss some potential systems where one
might be able to achieve these results experimentally.
