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

## TL;DR

This paper analyzes the vacuum phase structure of a 3D two-flavor Gross-Neveu model, revealing how the dominance of quark-antiquark or diquark condensates depends on the coupling ratio, with no coexistence phase.

## Contribution

It provides a detailed effective potential analysis of condensate phases in a 3D model and compares these findings with lower and higher-dimensional cases.

## Key findings

- Pure diquark condensate phase for G_S/H_P > 2/3
- Pure quark-antiquark condensate phase for G_S/H_P < 2/3
- No coexistence of both condensates in vacuum

## Abstract

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.