scholarly journals The RG flow of Nambu–Jona-Lasinio model at finite temperature and density

2015 ◽  
Vol 30 (27) ◽  
pp. 1550180 ◽  
Author(s):  
Ken-Ichi Aoki ◽  
Masatoshi Yamada
Keyword(s):  
Renormalization Group ◽  
Phase Boundary ◽  
Finite Temperature ◽  
Quantum Corrections ◽  
Coupling Constant ◽  
Density Region ◽  
Chiral Phase ◽  
Functional Renormalization Group ◽  
Njl Model ◽  
High Density Region

We study the Nambu–Jona-Lasinio model at finite temperature and finite density by using the functional renormalization group. The RG flows of the four-Fermi coupling constant in the NJL model are investigated. We obtain the chiral phase boundary in cases of the large-[Formula: see text] leading approximation and an improved approximation. The large-[Formula: see text] nonleading term at the vanishing temperature has a singularity at the Fermi surface. We show that the quantum corrections by the large-[Formula: see text] nonleading term largely influence the phase boundary at low temperature and high density region.

Studies on proper time regularization and the QCD chiral phase transition

2019 ◽  
Vol 34 (01) ◽  
pp. 1950003
Author(s):  
Yu-Qiang Cui ◽  
Zhong-Liang Pan
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Effective Mass ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Njl Model ◽  
The Difference

We investigate the finite-temperature and zero quark chemical potential QCD chiral phase transition of strongly interacting matter within the two-flavor Nambu–Jona-Lasinio (NJL) model as well as the proper time regularization. We use two different regularization processes, as discussed in Refs. 36 and 37, separately, to discuss how the effective mass M varies with the temperature T. Based on the calculation, we find that the M of both regularization schemes decreases when T increases. However, for three different parameter sets, quite different behaviors will show up. The results obtained by the method in Ref. 36 are very close to each other, but those in Ref. 37 are getting farther and farther from each other. This means that although the method in Ref. 37 seems physically more reasonable, it loses the advantage in Ref. 36 of a small parameter dependence. In addition, we also, find that two regularization schemes provide similar results when T [Formula: see text] 100 MeV, while when T is larger than 100 MeV, the difference becomes obvious: the M calculated by the method in Ref. 36 decreases more rapidly than that in Ref. 37.

The two-flavor NJL model with two-cutoff proper time regularization

2014 ◽  
Vol 29 ◽  
pp. 1460232 ◽  
Author(s):  
Zhu-Fang Cui ◽  
Yi-Lun Du ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Model Parameters ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Regularization Scheme ◽  
Njl Model

In this paper, we use the two-flavor Nambu–Jona-Lasinio model together with the proper time regularization that has both ultraviolet and infrared cutoffs to study the chiral phase transition at finite temperature and zero chemical potential. The involved model parameters in our calculation are determined in the traditional way. Our calculations show that the dependence of the results on the choice of the parameters are really small, which can then be regarded as an advantage besides such a regularization scheme is Lorentz invariant.

scholarly journals Finite-Temperature Spectral Functions from the Functional Renormalization Group

2014 ◽  
Author(s):  
Ralf-Arno Tripolt ◽  
Nils Strodthoff ◽  
Lorenz von Smekal ◽  
Jochen Wambach
Keyword(s):  
Renormalization Group ◽  
Finite Temperature ◽  
Spectral Functions ◽  
Functional Renormalization Group

scholarly journals Chiral phase boundary of QCD at finite temperature

2006 ◽  
Vol 2006 (06) ◽  
pp. 024-024 ◽  
Author(s):  
Jens Braun ◽  
Holger Gies
Keyword(s):  
Phase Boundary ◽  
Finite Temperature ◽  
Chiral Phase

scholarly journals Four Loop Scalar ϕ4 Theory Using the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Margaret Carrington ◽  
Christopher Phillips
Keyword(s):  
Renormalization Group ◽  
Effective Theory ◽  
Group Method ◽  
Coupling Constant ◽  
Loop Order ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Bare Coupling Constant ◽  
Effective Theories

We work with a symmetric scalar theory with quartic coupling in 4-dimensions. Using a 2PI effective theory and working at 4 loop order, we renormalize with a renormalization group method. All divergences are absorbed by one bare coupling constant and one bare mass which are introduced at the level of the Lagrangian. The method is much simpler than counterterm renormalization, and can be generalized to higher order nPI effective theories.

scholarly journals Functional renormalization group study of the critical region of the quark-meson model with vector interactions

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Renan Câmara Pereira ◽  
Rainer Stiele ◽  
Pedro Costa
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Critical Region ◽  
Entropy Density ◽  
Density Region ◽  
Functional Renormalization Group ◽  
Unphysical Region ◽  
Negative Entropy ◽  
First Order ◽  
Perturbative Method

Abstract The critical region of the two flavour quark-meson model with vector interactions is explored using the Functional Renormalization Group, a non-perturbative method that takes into account quantum and thermal fluctuations. Special attention is given to the low temperature and high density region of the phase diagram, which is very important to construct the equation of state of compact stars. As in previous studies, without repulsive vector interaction, an unphysical region of negative entropy density is found near the first order chiral phase transition. We explore the connection between this unphysical region and the chiral critical region, especially the first order line and spinodal lines, using also different values for vector interactions. We find that the unphysical negative entropy density region appears because the $$s=0$$s=0 isentropic line, near the critical region, is displaced from its $$T=0$$T=0 location. For certain values of vector interactions this region is pushed to lower temperatures and high chemical potentials in such way that the negative entropy density region on the phase diagram can even disappear. In the case of finite vector interactions, the location of the critical end point has a non-trivial behaviour in the $$T-\mu _B$$T-μB plane, which differs from that in mean field calculations.

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