EFFICIENT DESCRIPTION FOR π AND σ MESONS BY RESONATING MEAN-FIELD APPROXIMATION TO TWO-FLAVOR NAMBU-JONA-LASINIO MODEL

2006 ◽  
Vol 15 (05) ◽  
pp. 1087-1114 ◽  
Author(s):  
SEIYA NISHIYAMA ◽  
JOÃO DA PROVIDÊNCIA ◽  
OSAMU OHNO
Keyword(s):  
Order Parameter ◽  
Degrees Of Freedom ◽  
Decay Constant ◽  
Mean Field ◽  
Mass Term ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pion Decay ◽  
Pion Decay Constant ◽  
Njl Model

We have applied the resonating (Res-) mean-field approximation (MFA) to fermion systems with large quantum fluctuations over the usual MFA to a naive Nambu-Jona-Lasinio (NJL) model involving no current quark mass term. In our approach, as part of the model the normalization volume is kept finite, which plays an important role. This attempt has been quite successful in explaining the pion and sigma-meson masses, but the values of the order parameter for quark condensate and the pion decay constant are too small. This fact suggests us that the Res-MFA including no isospin causes such a problem. To avoid the serious drawback, if we naturally extend the NJL model to include two-flavor degrees of freedom and make an SU(2)f resonating Hartree-Fock (Res-HF) approximation, it is expected that the magnitudes of the order parameter and the pion decay constant are much improved. Using this extended NJL model, they are calculated again and both the numerical values [Formula: see text] and fπ reach good agreements with their experimental ones.

ANTIFERROMAGNETISM AND HOLE CONCENTRATION IN THE LINEAR SPIN WAVE APPROXIMATION OF THE t-J MODEL

1994 ◽  
Vol 08 (02) ◽  
pp. 131-136 ◽  
Author(s):  
A. BELKASRI ◽  
J.L. RICHARD
Keyword(s):  
Spin Wave ◽  
Order Parameter ◽  
Degrees Of Freedom ◽  
Hole Concentration ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic State ◽  
Wave Approximation ◽  
The Mean

The interplay between antiferromagnetic state and low doping regime is studied within the framework of the t-J model. The staggered magnetization is calculated in the mean field approximation by separating spin and charge degrees of freedom. We have obtained that this order parameter decreases with increasing doping and vanishes for some critical hole concentration.

A MEAN FIELD STUDY OF THE PHASE TRANSITIONS IN A CLASS OF SYSTEMS WITH COMPLEX ORDER PARAMETERS

1994 ◽  
Vol 08 (28) ◽  
pp. 3963-3986
Author(s):  
EVGENIA J. BLAGOEVA
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Order Parameter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Unconventional Superconductors ◽  
Complex Order ◽  
The Mean ◽  
Expansion Coefficients

A generalized Landau free energy for a complex order parameter expanded up to sixth-order is investigated using group theoretical arguments and the mean-field approximation. Results for the phase transitions that occur are presented. The phase diagram for all allowed values of the expansion coefficients is constructed with an emphasis placed on the influence of the anisotropy in the order parameter space. The results can be used in discussions of unconventional superconductors and modulated structural and magnetic orderings.

On the stability of two-flavor and three-flavor quark matter in quark stars within the framework of NJL model

2020 ◽  
Vol 35 (39) ◽  
pp. 2050321 ◽  
Author(s):  
Qianyi Wang ◽  
Tong Zhao ◽  
Hongshi Zong
Keyword(s):  
Quark Matter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Quark Stars ◽  
Njl Model ◽  
The Stability ◽  
Chiral Susceptibility ◽  
Strong Interaction Matter

Following our recently proposed self-consistent mean field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli–Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.

scholarly journals 1/Nc EXPANSION FOR THE PARTITION FUNCTION IN FOUR-FERMION MODELS

1996 ◽  
Vol 11 (19) ◽  
pp. 1579-1587 ◽  
Author(s):  
A. BARDUCCI ◽  
R. CASALBUONI ◽  
M. MODUGNO ◽  
G. PETTINI ◽  
R. GATTO
Keyword(s):  
Partition Function ◽  
Low Temperatures ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Field Approximation ◽  
Functional Integral ◽  
Mean Field Approximation ◽  
Thermodynamical Potential ◽  
Low Mass ◽  
The Mean

We present a derivation of the bosonic contribution to the thermodynamical potential of four-fermion models by means of a 1/N c -expansion of the functional integral defining the partition function. This expansion turns out to be particularly useful in correcting the mean field approximation especially at low temperatures, where the relevant degrees of freedom are low-mass bosonic excitations (pseudo-Goldstones).

SPIN-CARRYING SLAVE BOSON REPRESENTATION FOR STRONGLY CORRELATED FERMION SYSTEMS

1989 ◽  
Vol 03 (12) ◽  
pp. 1833-1842
Author(s):  
P. Wölfle
Keyword(s):  
Hubbard Model ◽  
Anderson Model ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Strongly Correlated ◽  
Dynamical Correlation ◽  
Fermion Systems ◽  
Boson Representation

We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.

THE NEW MEAN FIELD RENORMALIZATION GROUP FROM EFFECTIVE FIELD THEORY

1995 ◽  
Vol 09 (24) ◽  
pp. 1617-1621 ◽  
Author(s):  
F. O. COELHO ◽  
J. A. PLASCAK
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Order Parameter ◽  
Mean Field ◽  
Previous Treatment ◽  
Field Approximation ◽  
Effective Field ◽  
Mean Field Approximation ◽  
Field Renormalization

The new mean field renormalization group is used to study the Ising model through the calculation of the order parameter by means of the effective field theory based on Callen–Suzuki identity. By considering one- and two-spin clusters, better results are obtained when compared to the previous treatment using the usual mean field approximation.

scholarly journals GAMOW–TELLER SUM RULE IN RELATIVISTIC NUCLEAR MODELS

2006 ◽  
Vol 21 (12) ◽  
pp. 935-946 ◽  
Author(s):  
HARUKI KURASAWA ◽  
TOSHIO SUZUKI
Keyword(s):  
Degrees Of Freedom ◽  
Random Phase ◽  
Mean Field ◽  
Field Approximation ◽  
Point Of View ◽  
Mean Field Approximation ◽  
Sum Rule ◽  
Relativistic Mean Field ◽  
Relativistic Corrections ◽  
Gamow Teller

Relativistic corrections are investigated to the Gamow–Teller (GT) sum rule with respect to the difference between the β- and β+ transition strengths in nuclei. Since the sum rule requires the complete set of the nuclear states, the relativistic corrections come from the anti-nucleon degrees of freedom. In the relativistic mean field approximation, the total GT strengths carried by the nucleon sector is quenched by about 12% in nuclear matter, while by about 8% in finite nuclei, compared to the sum rule value. The coupling between the particle-hole states with the nucleon–antinucleon states is also discussed with the relativistic random phase approximation, where the divergence of the response function is renormalized with use of the counterterms in the Lagrangian. It is shown that the approximation to neglect the divergence, like the no-sea approximation extensively used so far, is unphysical, from the sum-rule point of view.

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