Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio/Gross-Neveu Model at Finite Temperature and Chemical Potential

Kodama, Hiroaki; Sumi, Jun–Ichi

doi:10.1143/ptp.103.393

Cited by 8 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also spontaneous symmetry breaking can be explicitly studied if we replace µ 2 σ φ ⋆ φ by an effective potential U (φ ⋆ φ) which may have a minimum for φ = 0. This approach has been followed in previous studies [35,36,37,38]. In the present paper we will briefly pursue only the extension (25) since our main focus is the issue of the Fierz ambiguity.…”

Section: Bosonic Flowmentioning

confidence: 99%

Flow equations without mean field ambiguity

2003

View full text Add to dashboard Cite

We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory often shows a basic ambiguity related to the possibility to perform Fierz transformations. The results may then depend strongly on an unphysical parameter which reflects the choice of the mean field, thus limiting the reliability. This ambiguity is absent for Schwinger-Dyson equations or fermionic renormalization group equations. Also renormalization group equations in a partially bosonized setting can overcome the Fierz ambiguity if the truncation is chosen appropriately. This is reassuring since the partially bosonized renormalization group approach constitutes a very promising basis for the explicit treatment of condensates and spontaneous symmetry breaking even for situations where the bosonic correlation length is large.

show abstract

Section: Bosonic Flowmentioning

confidence: 99%

Flow equations without mean field ambiguity

2003

View full text Add to dashboard Cite

show abstract

“…However if we work with the motion of string, the verticality of string does not mean anything singular; it is just vertical. Some authors define inverse four-fermi coupling constant g(t) ≡ 1/ G (t), which satisfies the following RG equation [18],…”

Section: /29mentioning

confidence: 99%

Weak solution of the non-perturbative renormalization group equation to describe the dynamical chiral symmetry breaking

Aoki,

Kumamoto,

Sato

2014

Preprint

View full text Add to dashboard Cite

We analyze the dynamical chiral symmetry breaking (DχSB) in the Nambu-Jona-Lasinio (NJL) model by using the non-perturbative renormalization group (NPRG) equation. The equation takes a form of two-dimensional partial differential equation for the multifermion effective interactions V (x, t) where x is ψψ operator and t is the logarithm of the renormalization scale. The DχSB occurs due to the quantum corrections, which means it emerges at some finite t c in the mid of integrating the equation with respect to t. At t c some singularities suddenly appear in V which is compulsory in the spontaneous symmetry breakdown. Therefore there is no solution of the equation beyond t c . We newly introduce the notion of weak solution to get the global solution including the infrared limit t → ∞ and investigate its properties. The obtained weak solution is global and unique, and it perfectly describes the physically correct vacuum even in case of the first order phase transition appearing in finite density medium. The key logic of deduction is that the weak solution we defined automatically convexifies the effective potential when treating the singularities.

show abstract

Phase structure of NJL model with weak renormalization group

2018

View full text Add to dashboard Cite

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 (σ; t) is given as a partial differential equation, where σ :=ψψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale t c , V (σ; 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 DχSB 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.

show abstract

Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio/Gross-Neveu Model at Finite Temperature and Chemical Potential

Cited by 8 publications

References 16 publications

Flow equations without mean field ambiguity

Flow equations without mean field ambiguity

Weak solution of the non-perturbative renormalization group equation to describe the dynamical chiral symmetry breaking

Phase structure of NJL model with weak renormalization group

Contact Info

Product

Resources

About