  High density phase transitions in a 4 dimensional Nambu-Jona-Lasinio model
containing a single symmetry breaking order parameter coming from the
fermion-antifermion condensates are researched and expounded by means of both
the gap equation and the effective potential approach. The phase transitions
are proven to be second order at a high temperature $T$; however at T=0, they
are first- or second- order, depending on whether $\Lambda/m(0)$, the ratio of
the momentum cutoff $\Lambda$ in the fermion loop integrals to the dynamical
fermion mass $m(0)$ at zero temperature, is less than 3.387 or not. The former
condition can not be satisfied in some models. The discussions further show
complete effectiveness of the critical analysis based on the gap equation for
second order phase transitions including determination of the condition of
their occurrence.
