Phenomenological theory of two-dimensional quantum liquids

A phenomenological theory is presented for two-dimensional quantum liquids in terms of the Fermi surface geometry. It is shown that there is a one-to-one correspondence between the properties of an interacting electron system and its corresponding Fermi surface. By doing this, the concept of Fermi surface is generalized to include different topologies. It is shown that for a Fermi liquid the corresponding Fermi surface is rough. In the presence of a condensate, the Fermi surface is faceted, while for a ferromagnetc instability, the Fermi surface becomes a frozen solid. I also determine the surface tension, the step free energy, low lying excitations and other surface and transport properties of the Fermi surface. The different transitions between these phases are also determined. A non-Fermi liquid phase is shown to be a pre-roughening state of the Fermi surface, the properties of which are briefly analyzed.