  We investigate the properties of the ground state of strong coupling lattice
QCD at finite density. Our starting point is the effective Hamiltonian for
color singlet objects, which looks at lowest order as an antiferromagnet, and
describes meson physics with a fixed baryon number background. We concentrate
on uniform baryon number backgrounds (with the same baryon number on all
sites), for which the ground state was extracted in an earlier work, and
calculate the dispersion relations of the excitations. Two types of Goldstone
boson emerge. The first, antiferromagnetic spin waves, obey a linear dispersion
relation. The others, ferromagnetic magnons, have energies that are quadratic
in their momentum. These energies emerge only when fluctuations around the
large-N_c ground state are taken into account, along the lines of ``order from
disorder'' in frustrated magnetic systems. Unlike other spectrum calculations
in order from disorder, we employ the Euclidean path integral. For comparison,
we also present a Hamiltonian calculation using a generalized
Holstein-Primakoff transformation. The latter can only be constructed for a
subset of the cases we consider.
