From relativistic quantum fields to condensed matter and back again: updating the Gross-Neveu phase diagram

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.