Novel phases of planar fermionic systems

We discuss a family of planar (two-dimensional) systems with the following phase structure: a Fermi liquid, which goes via a second-order transition (with a nonclassical exponent even in the mean field) to an intermediate, inhomogeneous state (with nonstandard ordering momentum), which in turn goes via a first-order transition to a state with a canonical order parameter. We analyse two examples: (i) a superconductor in a parallel magnetic field for which the inhomogeneous state is obtained for 1.86T_c<or approximately=B<or approximately=1.86 square 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) spinless (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 discuss the experimental conditions for realizing and observing these phases and the renormalization group approach to the transitions.