scholarly journals TO WHAT EXTENT DOES THE SELF-CONSISTENT MEAN-FIELD EXIST?

2006 ◽  
Vol 15 (05) ◽  
pp. 1141-1148 ◽  
Author(s):  
LU GUO ◽  
FUMIHIKO SAKATA ◽  
EN-GUANG ZHAO ◽  
J. A. MARUHN
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Energy Difference ◽  
The Self ◽  
Fermion System ◽  
Avoided Crossing ◽  
Self Consistent ◽  
The Mean ◽  
The Many ◽  
First Time

A non-convergent difficulty near level-repulsive region is discussed within the self-consistent mean-field theory. It is shown by numerical and analytic studies that the mean-field is not realized in the many-fermion system when quantum fluctuations coming from two-body residual interaction and quadrupole deformation are larger than an energy difference between two avoided crossing orbits. An analytic condition indicating a limitation of the mean-field concept is derived for the first time.

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.

Bilayered Spin-S Heisenberg Model in Fractional Dimensions

1998 ◽  
Vol 12 (18) ◽  
pp. 1809-1812 ◽  
Author(s):  
K. K. Ng
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Ground State ◽  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
The Self ◽  
Self Consistent ◽  
Ferromagnetic Heisenberg Model ◽  
Fractional Dimensions

The ground state and the phase transitions of the bilayered spin-S anti-ferromagnetic Heisenberg model were studied by Ng et al.1 by using the Schwinger boson mean field theory. In this paper, an analytic continuation of the self-consistent equations is carried out in order to study the extension of the model to fractional dimensions from 1 to 2. Decreasing the dimensionality from 2 has an effect similar to that of decreasing the spin S. The corresponding phase diagram and phase transition will also be discussed.

On the self-consistent mean field theory for polar-polarizable fluids

1986 ◽  
Vol 57 (2) ◽  
pp. 337-349 ◽  
Author(s):  
G.N. Patey ◽  
D. Levesque ◽  
J.J. Weis
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
The Self ◽  
Self Consistent

COEXISTENCE OF FERROMAGNETISM AND SUPERCONDUCTIVITY IN THE TWO-DIMENSIONAL FERROMAGNETIC t–J MODEL

2003 ◽  
Vol 17 (27n28) ◽  
pp. 1417-1424
Author(s):  
FAN YANG ◽  
YUPENG WANG ◽  
RUSHAN HAN
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
P Wave ◽  
Hole Doping ◽  
Cooper Pairs ◽  
Two Dimensional ◽  
Self Consistent ◽  
The Mean ◽  
Theoretical Results

The two-dimensional ferromagnetic t–J model is studied in the framework of slave-boson mean field theory. After solving the mean field self-consistent equations, we find that there exists a hole-doping region δ1<δ<δ2 in which p-wave superconductivity and ferromagnetism coexist. There also exists a T* line, under which pre-paired p-wave cooper pairs appear. The similarity and differences between our theoretical results and the experimental ones made for UGe 2 are compared.

scholarly journals Remarks on the mean-field theory based on the SO(2N + 1) Lie algebra of the fermion operators

2019 ◽  
Vol 16 (12) ◽  
pp. 1950184
Author(s):  
Seiya Nishiyama ◽  
João da Providência
Keyword(s):  
Field Theory ◽  
Density Matrix ◽  
Lie Algebra ◽  
Mean Field Theory ◽  
Mean Field ◽  
Algebraic Theory ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Mean

Toward a unified algebraic theory for mean-field Hamiltonian describing paired- and unpaired-mode effects, in this paper, we propose a generalized Hartree–Bogoliubov mean-field Hamiltonian in terms of fermion pair and creation-annihilation operators of the [Formula: see text] Lie algebra. We diagonalize the generalized Hartree–Bogoliubov mean-field Hamiltonian and throughout its diagonalization we can first obtain the unpaired mode amplitudes which are given by the self-consistent field parameters appeared in the Hartree–Bogoliubov theory together with the additional self-consistent field parameter in the generalized Hartree–Bogoliubov mean-field Hamiltonian and by the parameter specifying the property of the [Formula: see text] group. Consequently, it turns out that the magnitudes of these amplitudes are governed by such parameters. Thus, it becomes possible to make clear a new aspect of such results. We construct the Killing potential in the coset space [Formula: see text] on the Kähler symmetric space which is equivalent to the generalized density matrix. We show another approach to the fermion mean-field Hamiltonian based on such a generalized density matrix. We derive an [Formula: see text] generalized Hartree–Bogoliubov mean-field Hamiltonian operator and a modified Hartree–Bogoliubov eigenvalue equation. We discuss on the mean-field theory related to the algebraic mean-field theory based on the generalized density matrix and the coadjoint orbit leading to the nondegenerate symplectic form.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models
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