The Hubbard model at half-filling, part III: the lower bound on the   self-energy
  We complete the proof that the two-dimensional Hubbard model at half-filling is not a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing a lower bound on a second derivative in momentum of the first non-trivial self-energy graph. 
Stephane Afchain, Jacques Magnen and Vincent Rivasseau