Evaluation of Effective Potential for Gross-Neveu Model with Tadpole Diagram Method

1984 ◽  
Vol 3 (1) ◽  
pp. 59-71
Author(s):  
Wang Rhung-tai ◽  
Ni Guang-jiong
Keyword(s):  
Effective Potential ◽  
Diagram Method ◽  
Tadpole Diagram ◽  
Gross Neveu Model

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.

scholarly journals ON THERMAL PHASE STRUCTURE OF DEFORMED GROSS–NEVEU MODEL

1996 ◽  
Vol 11 (39n40) ◽  
pp. 3091-3102 ◽  
Author(s):  
H.-T. SATO ◽  
H. TOCHIMURA
Keyword(s):  
Field Theory ◽  
Symmetry Breaking ◽  
Effective Potential ◽  
Phase Structure ◽  
Chiral Symmetry Breaking ◽  
Two Dimensional ◽  
Polymer Model ◽  
Pauli Matrices ◽  
Thermal Phase ◽  
Gross Neveu Model

We illustrate the phase structure of a deformed two-dimensional Gross–Neveu model which is defined by undeformed field contents plus deformed Pauli matrices. This deformation is based on two motives to find a more general polymer model and to estimate how q-deformed field theory affects on its effective potential. Some regions where chiral symmetry breaking and restoration take place repeatedly as temperature increasing are found.

scholarly journals HEAVISIDE TRANSFORM OF THE EFFECTIVE POTENTIAL IN THE GROSS-NEVEU MODEL

1996 ◽  
Vol 11 (35) ◽  
pp. 2793-2803
Author(s):  
HIROFUMI YAMADA
Keyword(s):  
Effective Potential ◽  
Infinite Order ◽  
Small Mass ◽  
Heaviside Function ◽  
Dynamical Mass ◽  
Perturbative Series ◽  
Mass Expansion ◽  
Gross Neveu Model

Unconventional way of handling the perturbative series is presented with the help of Heaviside transformation with respect to the mass. We apply Heaviside transform to the effective potential in the massive Gross-Neveu model and carry out perturbative approximation of the massless potential by dealing with the resulting Heaviside function. We find that accurate values of the dynamical mass can be obtained from the Heaviside function at finite orders where just several diagrams are incorporated. We prove that our approximants converge to the exact massless potential in the infinite order. Small mass expansion of the effective potential can also be obtained in our approach.

scholarly journals RENORMALIZATION GROUP EFFECTS IN THE CONFORMAL SECTOR OF 4D QUANTUM GRAVITY WITH MATTER

1994 ◽  
Vol 09 (22) ◽  
pp. 2041-2047 ◽  
Author(s):  
S. ODINTSOV ◽  
R. PERCACCI
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Quantum Gravity ◽  
Effective Potential ◽  
Gauge Coupling ◽  
Liouville Theory ◽  
Gross Neveu Model ◽  
Group Effects

We discuss the “gravitationally dressed” beta functions in the Gross-Neveu model interacting with 2d Liouville theory and in SU(N) gauge theory interacting with the conformal sector of 4d quantum gravity. Among the effects we suggest one may feel that the gravitational dressing are the minimum of the effective potential and the running of the gauge coupling.

Three-loop β function(s) and effective potential in the Gross-Neveu model

1991 ◽  
Vol 212 (2) ◽  
pp. 371-401 ◽  
Author(s):  
Cristina Luperini ◽  
Paolo Rossi
Keyword(s):  
Effective Potential ◽  
Β Function ◽  
Gross Neveu Model

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.

THE 2D GROSS–NEVEU MODEL BEYOND LARGE-N IN THE OPTIMIZED PERTURBATION THEORY

2007 ◽  
Vol 16 (09) ◽  
pp. 2798-2801 ◽  
Author(s):  
JEAN-LOÏC KNEUR ◽  
MARCUS BENGHI PINTO ◽  
RUDNEI O. RAMOS
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Effective Potential ◽  
Theory Method ◽  
Large N ◽  
Gross Neveu Model

In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross–Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.

THE EFFECTIVE ACTION FOR THE THIRRING GROSS-NEVEU MODEL IN (2+1) DIMENSIONS

1994 ◽  
Vol 09 (13) ◽  
pp. 1183-1188
Author(s):  
E.R. BEZERRA DE MELLO ◽  
R.F. RIBEIRO
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Three Dimensional ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Leading Order ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Dirac Spinors ◽  
Gross Neveu Model

We obtain in the leading order of 1/N expansion, the fermion-fermion effective potential for the three-dimensional model of (N) massless Dirac spinors with a general current and scalar quadrilinear self-interaction. Analyzing the Schrödinger equation in the presence of the nonrelativistic limit of this potential, we show that this system presents a fermionfermion bound state.

GROSS-NEVEU MODEL IN CURVED SPACE-TIME: THE EFFECTIVE POTENTIAL AND CURVATURE-INDUCED PHASE TRANSITION

1989 ◽  
Vol 04 (01) ◽  
pp. 143-149 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA
Keyword(s):  
Phase Transition ◽  
Gravitational Field ◽  
Constant Curvature ◽  
Effective Potential ◽  
Broken Symmetry ◽  
Curved Space ◽  
External Gravitational Field ◽  
Constant Curvature Space ◽  
The One ◽  
Gross Neveu Model

The Gross-Neveu model in external gravitational field has been considered. The Green's function in constant curvature space has been found, whereby one has obtained the one-loop effective potential. It has been shown that the restoration of spontaneously broken symmetry occurs in the form of the second order curvature-induced phase transition.

Sign in / Sign up

Export Citation Format

Share Document