Oscillating Effects in the Nambu -- Jona-Lasinio Model

Phase structure of the four dimensional Nambu -- Jona-Lasinio model has been investigated in two cases: 1) in nonsimply connected space-time of the form $R^3\times S^1$ (space coordinate is compactified and the length of the circle $S^1$ is $L$) with nonzero chemical potential $\mu$ and 2) in Minkowski space-time at nonzero values of $\mu,H$, where $H$ is the external magnetic field. In both cases on phase portraits of the model there are infinitly many massless chirally symmetric phases as well as massive ones with spontaneously broken chiral invariance. Such phase structure leads unavoidably to oscillations of some physical parameters at $L\to\infty$ or $H\to 0$, including magnetization, pressure and particle density of the system as well as quark condensate and critical curve of chiral phase transitions.