  This is a companion paper to cond-mat/9907130. Using the method of continuous
renormalization group around the Fermi surface and the results of
cond-mat/9907130, we achieve the proof that a two-dimensional jellium
interacting system of Fermions at low temperature T is a Fermi liquid (analytic
in the coupling constant g) for g < const./|log T| and satisfying uniform
bounds on the first and second derivatives of the selfenergy. This proves that
in two dimensions the transition temperature (if any) must be non-perturbative,
and is a step in the program of rigorous study of the BCS phase transition
using methods of constructive field theory.
