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

• Published in: Annals of physics Vol. 314; no. 2; pp. 425 - 447
• Main Authors: Schnetz, Oliver, Thies, Michael, Urlichs, Konrad
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-12-2004
• Subjects: Gross–Neveu model; Phase structure; 11.10.Wx; 11.15.Kc; Phase structure; Gross–Neveu model
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2004.06.009

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 Schrödinger equation with the (single gap) Lamé 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–Fröhlich model and ferromagnetic superconductors.