  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. Phase transitions of
1st and 2nd orders and several tricritical points have been shown to exist on
phase diagrams of the model.
