Nesting effects on fermionic systems

We derive a general set of Poor Man's scaling equations and analyze the stability of gapless states in two-dimensional nested systems of spinless fermions. The effect of processes with momentum transfer parallel to the Fermi surface in destroying massless states is investigated. It will be shown that massless states may be stable but that due to these processes the system is placed near instabilities. We argue that the massless states correspond to a hybrid liquid, in between a Fermi and a Luttinger liquid. A superconductive instability is also shown to exist for purely repulsive interactions.