Magnetic catalysis and magnetic oscillations in the Nambu-Jona-Lasinio model

The phase structure of the four-dimensional Nambu-Jona-Lasinio model in the presence of a chemical potential μ and an external magnetic field H is investigated at comparatively small values of the bare coupling constant (G<G _c). It is shown that only for magnetic-field strengths in excess of some critical value H _c(μ) does the magnetic field induce a spontaneous breakdown of chiral symmetry. On the phase portrait of the model, there are infinitely many massless chiral-invariant phases; in addition, there is one massive phase characterized by spontaneously broken chiral invariance. It is because of this phase structure of the system that some physical features of its ground state, including magnetization, pressure, and particle density, oscillate as H → 0. Changes in the vacuum properties of the model are accompanied by first-or second-order phase transitions.