  We study the effective Hamiltonian for strong-coupling lattice QCD in the
case of non-zero baryon density. In leading order the effective Hamiltonian is
a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and
the spins belong to a representation that depends on the local baryon number.
Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to
U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model
which we analyze in a 1/N_c expansion. In the vacuum sector we recover
spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn
theories. For non-zero baryon density we study the nearest-neighbor theory
only, and show that the pattern of spontaneous symmetry breaking depends on the
baryon density.
