Four-Fermion Theories with Exact Chiral Symmetry in Three Dimensions

Understand

We investigate a class of four-fermion theories which includes well-known models like the Gross-Neveu model and the Thirring model.

• In three spacetime dimensions, they are used to model interesting solid state systems like high temperature superconductors and graphene.
• Additionally, they serve as toy models to study chiral symmetry breaking (CSB).
• For any number of fermion flavours the Gross-Neveu model has a broken and a symmetric phase, while the existence of a broken phase in the Thirring model depends on the number of flavours.