Using the method of continuous constructive renormalization group around the Fermi surface, we prove that a jellium two-dimensional interacting system of fermions at low temperature $T$ is analytic in the coupling constant $\lambda$ for $|\lambda ||\log T|\le K$, where $K$ is some numerical constant and $T$ is the temperature. In that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior seen in Fermi liquids but, in particular, not in Luttinger liquids. Our results also prove that in 2D any transition temperature must be nonperturbative in the coupling constant, a result expected on physical grounds. The proof exploits specific momentum conservation rules in two dimensions.

• Received 12 November 1999

DOI:https://doi.org/10.1103/PhysRevLett.85.361