scholarly journals Quality of the mean-field approximation: A low-order generalization yielding realistic critical indices for three-dimensional Ising-class systems

2002 ◽  
Vol 66 (5) ◽  
Author(s):  
A. N. Rubtsov
Keyword(s):  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Critical Indices ◽  
The Mean ◽  
Low Order

Critical indices for spin correlation functions in ferromagnetic films

1979 ◽  
Vol 57 (10) ◽  
pp. 1686-1698 ◽  
Author(s):  
G. Gumbs ◽  
A. Griffin
Keyword(s):  
Correlation Functions ◽  
Finite Thickness ◽  
Mean Field ◽  
Spin Correlation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Critical Indices ◽  
The Mean

Using the Ginzburg–Landau–Wilson (GLW) Hamiltonian, we obtain, with the mean-field approximation, explicit expressions for the spin–spin correlation function χ(z,z′) of a film of thickness L above the phase transition temperature Tc and the spontaneous magnetization [Formula: see text] below Tc. The boundaries are treated using a temperature-independent extrapolation length Λ. From our results, we verify explicitly that for finite L, the critical indices associated with the spin–spin correlation functions and the surface magnetization are identical with those for the analogous two-dimensional system, for both the ordinary (Λ > 0) and surface (Λ < 0) transitions. Our model results nicely exhibit the fact that as long as L is finite, when the temperature T approaches sufficiently close to Tc, there is a crossover from behaviour characteristic of a single surface to two-dimensional behaviour. Within the one-loop, Hartree self-consistent field approximation, we study the effects of mode–mode coupling on the surface layer susceptibility in films of varying thicknesses. The singular behaviour obtained in the mean-field approximation is found to be completely removed in systems of finite thickness, the susceptibilities only exhibiting a finite cusp at the transition.

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.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals UNDERSTANDING MAGNETIC INSTABILITY IN GAPLESS SUPERCONDUCTORS

2006 ◽  
Vol 21 (04) ◽  
pp. 910-913 ◽  
Author(s):  
Mei Huang
Keyword(s):  
Superconducting State ◽  
Phase Fluctuation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Bcs Theory ◽  
Magnetic Instability ◽  
Fermi Surfaces ◽  
Strong Phase ◽  
The Mean

Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected. The mean-field BCS theory describes very well the strongly coherent or rigid superconducting state. With the increase of mismatch between the Fermi surfaces of pairing fermions, the phase fluctuation plays more and more important role, and "soften" the superconductor. The strong phase fluctuation will eventually quantum disorder the superconducting state, and turn the system into a phase-decoherent pseudogap state.

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