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

2000 ◽  
Vol 103 (2) ◽  
pp. 393-410 ◽  
Author(s):  
H. Kodama ◽  
J.-I. Sumi
Keyword(s):  
Renormalization Group ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Perturbative Renormalization ◽  
Gross Neveu Model

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

scholarly journals ON PHASE DIAGRAM OF GROSS-NEVEU MODEL AT FINITE TEMPERATURE, DENSITY AND CONSTANT CURVATURE

1995 ◽  
Vol 10 (24) ◽  
pp. 1777-1785 ◽  
Author(s):  
SHINYA KANEMURA ◽  
HARU-TADA SATO
Keyword(s):  
Constant Curvature ◽  
Finite Temperature ◽  
Critical Line ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Critical Surface ◽  
Leading Order ◽  
Third Order ◽  
Curvature Approximation ◽  
Gross Neveu Model

We discuss a phase structure of chiral symmetry breaking in the Gross-Neveu model at finite temperature, density and constant curvature. The effective potential is evaluated in the leading order of the 1/N-expansion and in a weak curvature approximation. The third-order critical line is found on the critical surface in the parameter space of temperature, chemical potential and constant curvature.

PHASE DIAGRAM OF THE THREE DIMENSIONAL FOUR FERMI MODEL WITH FINITE N CORRECTIONS

2007 ◽  
Vol 16 (09) ◽  
pp. 2802-2805 ◽  
Author(s):  
JEAN-LOÏC KNEUR ◽  
MARCUS BENGHI PINTO ◽  
RUDNEI O. RAMOS ◽  
EDERSON STAUDT
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Perturbation Theory ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Fermi Model ◽  
Analytical Results ◽  
Theory Technique ◽  
Gross Neveu Model

We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.

scholarly journals The Gross-Neveu model at finite temperature and density

1987 ◽  
Vol 280 ◽  
pp. 289-303 ◽  
Author(s):  
F. Karsch ◽  
J. Kogut ◽  
H.W. Wyld
Keyword(s):  
Finite Temperature ◽  
Gross Neveu Model

STOCHASTIC FIELD THEORY AND RENORMALIZATION GROUP APPROACH TO CRITICAL BEHAVIORS IN THERMO FIELD DYNAMICS

1989 ◽  
Vol 04 (09) ◽  
pp. 2185-2210
Author(s):  
B. BHATTACHARYA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Finite Temperature ◽  
Internal Field ◽  
Point Of View ◽  
Internal Space ◽  
Theoretic Approach ◽  
Stochastic Field ◽  
Stochastic Fields ◽  
Renormalization Group Approach

We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.

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