Phase and amplitude fluctuations for the $l=2$ Pomeranchuk instability in two dimensions.

For a two-dimensional fermionic system, we analyze models that produce shape-distortion instabilities of the Fermi surface in the $l=2$ channel, leading to a non-Fermi liquid with nematic order. The finite-temperature phase diagram contains a transition of the Kosterlitz-Thouless type and a crossover at higher temperatures, corresponding respectively to the disordering of phase and amplitude degrees of freedom.