Phase diagram of the Gross-Neveu model: exact results and condensed matter precursors

摘要

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1 + 1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schrodinger equation with the (single gap) Lame potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Frohlich model and ferromagnetic superconductors. (C) 2004 Elsevier Inc. All rights reserved.