  We propose a fully microscopic theory of the anomalous normal state of the
attractive Hubbard model in the low-density limit that accounts for propagator
renormalization. Our analytical conclusions, which focus on the thermodynamic
instabilities contained in the self-consistent equations associated with our
formulation, have been verified by our comprehensive numerical study of the
same equations. The resulting theory is found to contain no transitions at
non-zero temperatures for all finite lattices, and we have confirmed, using our
numerical studies, that this behaviour persists in the thermodynamic limit for
low-dimensional systems.
