Phase structure of NJL model with weak renormalization group

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.

arXiv comment32 pages, 12 figures; Version published in Nuclear Physics B

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• QCD at finite temperature and density within the fRG approach: An overview
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Gravitational instantons and anomalous chiral symmetry breaking
• Axial anomaly and hadronic properties in a nuclear medium
• Functional renormalization group study of a four-fermion model with $CP$ violation
• QCD chiral phase diagram from weak functional renormalization group