NOVEL PHASES OF PLANAR FERMIONIC SYSTEMS

We discuss a family of planar (two-dimensional) systems with the follo wing phase structure: a Fermi liquid, which goes via a second-order tr ansition (with a nonclassical exponent even in the mean field) to an i ntermediate, inhomogeneous state (with nonstandard ordering momentum), which in turn goes via a first-order transition to a state with a can onical order parameter. We analyse two examples: (i) a superconductor in a parallel magnetic field for which the inhomogeneous state is obta ined for 1.86T(c) less than or similar to B less than or similar to 1. 86 root 2T(c) where T-c is the critical temperature (in kelvin) of the superconductor without a field and B is measured in tesla; and (ii) s pinless (or spin-polarized) fermions near half-filling where a similar , sizeable window (which grows in size with anisotropy) exists for the intermediate CDW phase at a momentum different from (pi, pi). We disc uss the experimental conditions for realizing and observing these phas es and the renormalization group approach to the transitions.