Renormalization of the 2-point function of the Hubbard model at   half-filling
  We prove that the two dimensional Hubbard model at finite temperature T and half-filling is analytic in the coupling constant in a radius at least $c/(\log T)^2$. We also study the self-energy through a new two-particle irreducible expansion and prove that this model is not a Fermi liquid, but a Luttinger liquid with logarithmic corrections. The techniques used are borrowed from constructive field theory so the result is mathematically rigorous and completely non-perturbative.   Together with earlier results on the existence of two dimensional Fermi liquids, this new result proves that the nature of interacting Fermi systems in two dimensions depends on the shape of the Fermi surface. 
Stephane Afchain, Jacques Magnen, Vincent Rivasseau