APPLICATION OF A NEW VARIATIONAL METHOD TO THE GROSS-NEVEU MODEL

1991 ◽  
Vol 06 (37) ◽  
pp. 3405-3412
Author(s):  
HIROFUMI YAMADA
Keyword(s):  
Variational Method ◽  
Effective Potential ◽  
Finite Temperature ◽  
Mean Field ◽  
Chiral Condensate ◽  
Field Analysis ◽  
Efficient Manner ◽  
The Mean ◽  
Gross Neveu Model

A new variational method proposed by Neveu is applied to the Gross-Neveu model. Chiral condensate is computed perturbatively at zero and finite temperature by the use of effective potential. At both temperatures the expected results in the mean field analysis, nonzero condensate at T=0 and restoration of γ5 symmetry at T≠0, are recovered in an efficient manner by calculating only a few lowest order diagrams.

scholarly journals APPROACH TO D-DIMENSIONAL GROSS–NEVEU MODEL AT FINITE TEMPERATURE AND CURVATURE

1996 ◽  
Vol 11 (10) ◽  
pp. 785-793 ◽  
Author(s):  
SHINYA KANEMURA ◽  
HARU-TADA SATO
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Effective Potential ◽  
Finite Temperature ◽  
Phase Structure ◽  
Critical Line ◽  
Chiral Symmetry Breaking ◽  
Leading Order ◽  
Third Order ◽  
Gross Neveu Model

We discuss phase structure of chiral symmetry breaking of the D-dimensional (2≤D≤3) Gross–Neveu model at finite temperature, density and constant curvature. We evaluate the effective potential in a weak background approximation to thermalize the model as well as in the leading order of the 1/N-expansion. A third-order critical line is observed similarly to the D=2 case.

EFFECTIVE P, T RESTORATION IN CHERN–SIMONS SUPERCONDUCTIVITY

1994 ◽  
Vol 08 (08n09) ◽  
pp. 561-570 ◽  
Author(s):  
S. S. MANDAL ◽  
S. RAMASWAMY ◽  
V. RAVISHANKAR
Keyword(s):  
Dielectric Constant ◽  
Magnetic Susceptibility ◽  
Normal State ◽  
Time Reversal ◽  
Finite Temperature ◽  
Narrow Range ◽  
Mean Field ◽  
Smooth Transition ◽  
The Mean ◽  
Chern Simons

We present an analysis of the finite temperature Chern–Simons superconductivity model within the mean field framework. Using analytical and numerical means we compute the changes in the magnetic susceptibility, conductivity, the dielectric constant, and the specific heat as the temperature is increased. Over a narrow range of temperatures the properties of the system show a smooth transition to the normal state. Accompanying this is the near vanishing of the off-diagonal conductivity, signifying the effective restoration of parity and time reversal symmetries.

scholarly journals Inhomogeneous chiral condensates in low-energy color-superconductivity models of QCD

2021 ◽  
Author(s):  
◽  
Philip Lakaschus
Keyword(s):  
Phase Diagram ◽  
Mean Field ◽  
Field Approximation ◽  
Chiral Condensate ◽  
Dispersion Relations ◽  
Mean Field Approximation ◽  
Color Superconductivity ◽  
Diquark Model ◽  
Coexistence Phase ◽  
The Mean

This thesis explores the phase diagrams of the Nambu--Jona-Lasinio (NJL) and quark-meson (QM) model in the mean-field approximation and beyond. The focus lies in the investigation of the interplay between inhomogeneous chiral condensates and two-flavor color superconductivity. In the first part of this thesis, we study the NJL model with 2SC diquarks in the mean-field approximation and determine the dispersion relations for quasiparticle excitations for generic spatial modulations of the chiral condensate in the presence of a homogeneous 2SC-diquark condensate, provided that the dispersion relations in the absence of color superconductivity are known. We then compare two different Ansätze for the chiral order parameter, the chiral density wave (CDW) and the real-kink crystal (RKC). For both Ansätze we find for specific diquark couplings a so-called coexistence phase where both the inhomogeneous chiral condensate and the diquark condensate coexist. Increasing the diquark coupling disfavors the coexistence phase in favor of a pure diquark phase. On the other hand, decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. In the second part of this thesis the functional renormalization group is employed to study the phase diagram of the quark-meson-diquark model. We observe that the region of the phase diagram found in previous studies, where the entropy density takes on unphysical negative values, vanishes when including diquark degrees of freedom. Furthermore, we perform a stability analysis of the homogeneous phase and compare the results with those of previous studies. We find that an increasing diquark coupling leads to a smaller region of instability as the 2SC phase extends to a smaller chemical potential. We also find a region where simultaneously an instability occurs and a non-vanishing diquark condensate forms, which is an indication of the existence of a coexistence phase in accordance with the results of the first part of this work.

Thermomagnetic Properties and Magnetocaloric Effect of R2Fe17C (R=Dy, Nd, Tb, Gd, Pr, Ho, Er) Compounds

2018 ◽  
Vol 1 (1) ◽  
pp. 268-278
Author(s):  
Ahmed Nagy ◽  
Samy H. Aly ◽  
Sherif Yehia ◽  
Tareq Hammad
Keyword(s):  
Magnetocaloric Effect ◽  
Mean Field ◽  
Entropy Change ◽  
Field Analysis ◽  
Magnetic Phase Transitions ◽  
Mean Field Model ◽  
Magnetocaloric Properties ◽  
The Mean ◽  
Thermomagnetic Properties ◽  
Critical Temperature Tc

We present a mean-field analysis, using the two-sublattice model, for the thermomagnetic and magnetocaloric properties of the R2Fe17C compounds, where R=Dy, Nd, Tb, Gd, Pr, Ho, Er and C is carbon.   The dependence of magnetization, magnetic heat capacity, magnetic entropy and isothermal entropy change ∆Sm, are calculated for magnetic fields up to 5T and for temperatures up to 700 K . Direct magnetocaloric effect is present for all compounds with maximum ∆Sm between 6.13-10.95 J/K. mole for an applied field change of 5T. It is found that Pr2Fe17C compound has the highest  ∆Sm of 10.95 J/K. mole at ∆H=5T and Tc=375 K. The inverse MCE is found in ferrimagnetic compounds, e.g. Gd2Fe17C, with ∆Sm= J/K mol at critical temperature Tc=623K and ∆Sm=  J/K mol at Neel temperature TN=136 K.  The calculated Arrott plots confirmed that the magnetic phase transitions in these compounds are of second order. The mean-field model proves its suitability for calculating the properties of the compounds under study.

A Contribution to the Mean-Field Analysis of Amorphous Magnets

1993 ◽  
Vol 179 (2) ◽  
pp. 551-556 ◽  
Author(s):  
Y. Millev ◽  
M. Fähnle
Keyword(s):  
Mean Field ◽  
Field Analysis ◽  
The Mean ◽  
Amorphous Magnets

QUADRUPOLE DEFORMATION IN NUCLEI AT FINITE TEMPERATURE

1998 ◽  
Vol 13 (33) ◽  
pp. 2705-2713 ◽  
Author(s):  
B. J. COLE ◽  
H. G. MILLER ◽  
R. M. QUICK
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Quadrupole Deformation ◽  
Mean Field Approximation ◽  
Zero Temperature ◽  
Average Deformation ◽  
The Mean ◽  
Shape Changes

The intrinsic quadrupole deformation has been calculated at finite temperature in 20 Ne both in the mean-field approximation and using an exact shell model diagonalization. The results support the view that the phase transition seen at finite temperature in mean-field calculations is not due to the change in nuclear shape from deformed to spherical, but rather is a collective-to-non-collective transition. Both calculations indicate that the average deformation of 20 Ne changes from β rms ≈0.31 at zero temperature to just over β rms =0.2 at T=3.0 MeV. The calculations also suggest that, in the mean-field approximation, the square of the quadrupole operator, Q[2]·Q[2], is a better indicator of shape changes than Q[2] itself.

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