From quantum electrodynamics to mean-field theory. II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation

1989 ◽  
Vol 22 (23) ◽  
pp. 3815-3828 ◽  
Author(s):  
P Chaix ◽  
D Iracane ◽  
P L Lions
Keyword(s):  
Field Theory ◽  
Quantum Electrodynamics ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Variational Stability ◽  
The Mean

scholarly journals Calculation of the Static Properties of Local Moment Systems by the Mean Field Method

1975 ◽  
Vol 28 (6) ◽  
pp. 685 ◽  
Author(s):  
AM Stewart
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Field Method ◽  
Local Moment ◽  
Mean Field Approximation ◽  
Static Properties ◽  
The Past ◽  
The Mean

It is demonstrated that two different methods which have been used in the past to calculate the static properties oflocal moment systems in the mean field approximation are incomplete. A proof is given of the correctness of another method that the author has used in several previous calculations. It is found that some exact and very general relationships exist between the conduction electron magnetization and the local moment magnetization even when it is not valid to treat the interactions between the magnetic atoms by mean field theory.

CAR-ORIENTED MEAN-FIELD THEORY REVISITED

2004 ◽  
Vol 18 (17) ◽  
pp. 887-894 ◽  
Author(s):  
YU-FUNG CHIEN ◽  
DING-WEI HUANG
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Density ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Stochastic Noise ◽  
Collective Effect ◽  
Self Consistent ◽  
The Mean

We study the Car-Oriented Mean-Field approximation (COMF) to the Nagel–Schreckenberg model in the case of v max =3. The self-consistent equations are obtained. The solution is reached by the method of iteration. When the stochastic noise is small, the numerical simulations can be well described by the mean-field theory. When the stochastic noise is large, the flux around critical density is overestimated. The overshooting of the free flow can be attributed to the collective effect of the stochastic noise.

MEAN-FIELD THEORY FOR LAYERED HIGH-TEMPERATURE SUPERCONDUCTORS

1988 ◽  
Vol 02 (05) ◽  
pp. 1059-1065 ◽  
Author(s):  
D. Baeriswyl ◽  
T. Schneider
Keyword(s):  
High Temperature Superconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
Interlayer Spacing ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pairing Mechanism ◽  
The Mean

Using the mean-field approximation we study a model for quasi-two-dimensional layered superconductors. The interlayer coupling, assumed to be mediated by a small electron hopping term, is found to leave Tc practically unaffected. Consequently, a three-dimensional pairing mechanism is required to explain the observed dependence of Tc on the average interlayer spacing in the Bi and Tl compounds.

The renormalization group (RG) approach: The critical theory near four dimensions

2021 ◽  
pp. 357-390
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gaussian Approximation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Flow Equations ◽  
Four Dimensions ◽  
The Mean

In Chapter 14, the singular behavior of ferromagnetic systems with O(N) symmetry and short-range interactions, near a second order phase transition has been determined in the mean-field approximation, which is also a quasi-Gaussian approximation. The mean-field approximation predicts a set of universal properties, properties independent of the detailed structure of the microscopic Hamiltonian, the dimension of space, and, to a large extent, of the symmetry of systems. However, the leading corrections to the mean-field approximation, in dimensions smaller than or equal to four, diverge at the critical temperature, and the universal predictions of the mean-field approximation cannot be correct. Such a problem originates from the non-decoupling of scales and leads to the question of possible universality. In Chapter 9, the question has been answered in four dimensions using renormalization theory, and related renormalization group (RG) equations. Moreover, below four dimensions, in an expansion around the mean-field, the most singular terms near criticality can be also formally recovered from a continuum, low-mass φ4 field theory. More generally, following Wilson, to understand universality beyond the mean-field approximation, it is necessary to build a general renormalization group in the form of flow equations for effective Hamiltonians and to find fixed points of the flow equations. Near four dimensions, the flow equations can be approximated by the renormalization group of quantum field theory (QFT), and the fixed points and critical behaviours derived within the framework of the Wilson-Fisher ϵ expansion.

scholarly journals THE CJT CALCULATION IN STUDYING NUCLEAR MATTER BEYOND MEAN FIELD APPROXIMATION

2008 ◽  
Vol 23 (21) ◽  
pp. 1769-1780 ◽  
Author(s):  
SONG SHU ◽  
JIA-RONG LI
Keyword(s):  
Field Theory ◽  
Nuclear Matter ◽  
Chemical Potential ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Medium Effects ◽  
Effective Masses ◽  
Walecka Model

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

ON THE VALIDITY OF MEAN-FIELD THEORY FOR ANYONS ON A LATTICE

1992 ◽  
Vol 06 (30) ◽  
pp. 1951-1960 ◽  
Author(s):  
A.A. OVCHINNIKOV ◽  
An. A. OVCHINNIKOV
Keyword(s):  
Large Deviation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Hard Core ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Phase Fluctuations ◽  
Fermi Statistics ◽  
The Mean ◽  
Field Approaches

We examine the validity of the mean-field approximation for anyons on a lattice at high density. The phase fluctuations for a large deviation from the Fermi statistics, in particular for the hard core bosons, are shown to be large. The importance of the phase fluctuations in different fermionic mean-field approaches for the antiferromagnetic Heisenberg model is stressed.

MEAN FIELD THEORY OF RVB

1988 ◽  
Vol 02 (05) ◽  
pp. 577-583 ◽  
Author(s):  
Hidetoshi FUKUYAMA
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Temperature Dependences ◽  
Physical Quantities

Implication of mean field approximation to RVB are explored and the temperature dependences of various physical quantities are evaluated. The results are discussed in the light of recent experiments.

scholarly journals Ferrimagnetism in the Mean-Field Approximation of the Mixed Spin-3/2 and Spin-5/2 Ising System

2015 ◽  
Vol 57 ◽  
pp. 114-121 ◽  
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Bogoliubov Inequality ◽  
The Mean

Using the Mean-field theory based on Bogoliubov inequality for the free energy, a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies is investigated. The free energy of a mixed spin Ising ferrimagnetic system from MF approximation of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and compensation points. In particular, we investigate the effect of a single-ion anisotropy on the magnetic properties including the compensation phenomenon, in order to clarify the characteristic behaviours in a series of molecular-based magnets . The phase diagram of the system is also discussed in the anisotropy dependence of transition temperature. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

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