  During the last few years, the phase diagram of the large N Gross-Neveu model
in 1+1 dimensions at finite temperature and chemical potential has undergone a
major revision. Here we present a streamlined account of this development,
collecting the most important results. Quasi-one-dimensional condensed matter
systems like conducting polymers provide real physical systems which can be
approximately described by the Gross-Neveu model and have played some role in
establishing its phase structure. The kink-antikink phase found at low
temperatures is closely related to inhomogeneous superconductors in the
Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at
hand, the Gross-Neveu model can now serve as a firm testing ground for new
algorithms and theoretical ideas.
