  The effective potential analysis indicates that, in a 3D two-flavor
Gross-Neveu model in vacuum, depending on less or bigger than the critical
value 2/3 of $G_S/H_P$, where $G_S$ and $H_P$ are respectively the coupling
constants of scalar quark-antiquark channel and pseudoscalar diquark channel,
the system will have the ground state with pure diquark condensates or with
pure quark-antiquark condensates, but no the one with coexistence of the two
forms of condensates. The similarities and differences in the interplay between
the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D
two-flavor four-fermion interaction models are summarized.
