  We study the spectral and magnetic properties of one-dimensional lattices
filled with 2 to 4 fermions (with spin 1/2) per lattice site. We use a
generalized Hubbard model that takes account all interactions on a lattice
site, and solve the many-particle problem by exact diagonalization. We find an
intriguing magnetic phase diagram which includes ferromagnetism, spin-one
Heisenberg antiferromagnetism, and orbital antiferromagnetism.
