  By critical analyses of the order parameter of symmetry breaking, we have
researched the phase transitions at high density in D=2 and D=3 Gross-Neveu
(GN) model and shown that the gap equation obeyed by the dynamical fermion mass
has the same effectivenesss as the effective potentials for such analyses of
all the second order and some special first order phase transitions. In the
meantime we also further ironed out a theoretical divergence and proven that in
D=3 GN model a first order phase transition does occur in the case of zero
temperature and finite chemical potential.
