Feedback effects and the self-consistent Thouless criterion of the attractive Hubbard model

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.