Phase Transitions in Four-Fermion Models

The most important advances in the physics of four-fermion theories are illustrated using the Nambu–Jona-Lasinio and Gross–Neveu models. Magnetic-field-catalyzed dynamical chiral symmetry breaking is considered, and the magnetic-field effect on the effective fermion mass is assessed. The models in question are used to interpret the recently discoveredPparity breaking in high-Tc superconductors. High-Tc materials are considered in which the superconducting transition can be interpreted within the Gross-Neveu model as due to the formation of Berezinskii–Kosterlitz–Thouless vortex–antivortex pairs. The generalized Gross–Neveu model with superconducting states is described. Examples are presented of nonperturbative kink–antikink solutions in the Gross–Neveu model, and their role in the restoration of spontaneously broken symmetry is discussed. A number of Gross–Neveu models on a sphere are considered with application to C60 fullerenes and related matrices with Tc = 117 K. It is shown that the curvature effect restores chiral symmetry according to the critical phase dependence rc(Tc).