  We study the $(1+1)$-dimensional chiral Gross-Neveu model on the lattice. At
finite density, analytic mean-field results predict the existence of
inhomogeneous condensates breaking both chiral symmetry and spacetime
symmetries spontaneously. We investigate the fate of these inhomogeneities for
two flavors and find remnant structural order, albeit with a decaying
amplitude. We also map out phase diagrams in the plane spanned by the chemical
potential and temperature for different lattice spacings and physical volumes.
Finally, we comment on the interpretation of our results in the light of
various no-go theorems.
