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.