# Phase structure of NJL model with weak renormalization group

## TL;DR

This paper employs the functional renormalization group to analyze the chiral phase structure of the NJL model at finite temperature and density, introducing a weak solution method to track RG flows beyond phase transition points.

## Contribution

It introduces a weak solution approach to the RG equation, enabling analysis of RG flows after chiral symmetry breaking in the NJL model.

## Key findings

- Successfully captures vacuum structures and critical phenomena.
- Provides a detailed chiral phase diagram.
- Demonstrates the effectiveness of weak solutions in RG analysis.

## Abstract

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.