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 regarding the thermodynamic instabilities contained in the self-consistent equations associated with this 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.

@article{
  title = {Feedback effects and the self-consistent Thouless criterion of the attractive Hubbard model},
  author = {Beach, K. S. D. and Gooding, R. J. and Marsiglio, F.},
  journal = {Physics Letters A},
  volume = {282},
  number = {4--5},
  pages = {319--324},
  year = {2001},
  issn = {0375-9601},
  doi = {10.1016/S0375-9601(01)00201-8},
  url = {http://www.sciencedirect.com/science/article/pii/S0375960101002018}
}