Quark-Antiquark and Diquark Condensates in Vacuum in a 3D Two-Flavor Gross-Neveu Model

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 $G_S\mathrm{/}{H}_P$, 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.