Gross-Neveu model, a theory of 2d interacting fermions, shares many features with QCD, such as chiral symmetry breaking and dynamical mass transmutation, and also has a similar phase diagram. As the mean-field (large-N) approximation indicates, the model develops a crystalline phase at low temperature and sufficiently high density, as a consequence of Peierls instability.  Taken at face value, this contradicts Coleman-Mermin-Wagner  theorem. To resolve this issue one can explore the Gross-Neveu model by the exact methods of Bethe ansatz.