1,145 research outputs found
Gell-Mann - Low Function in QED for the arbitrary coupling constant
The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure
constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha
with \alpha\approx 1, \beta_\infty\approx 1.Comment: 5 pages, PD
Quantum Electrodynamics at Extremely Small Distances
The asymptotics of the Gell-Mann - Low function in QED can be determined
exactly, \beta(g)= g at g\to\infty, where g=e^2 is the running fine structure
constant. It solves the problem of pure QED at small distances L and gives the
behavior g\sim L^{-2}.Comment: Latex, 6 pages, 1 figure include
Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions
According to the available publications, the field theoretical
renormalization group (RG) approach in the two-dimensional case gives the
critical exponents that differ from the known exact values. This fact was
attempted to explain by the existence of nonanalytic contributions in the RG
functions. The situation is analysed in this work using a new algorithm for
summing divergent series that makes it possible to analyse dependence of the
results for the critical exponents on the expansion coefficients for RG
functions. It has been shown that the exact values of all the exponents can be
obtained with a reasonable form of the coefficient functions. These functions
have small nonmonotonities or inflections, which are poorly reproduced in
natural interpolations. It is not necessary to assume the existence of singular
contributions in RG functions.Comment: PDF, 11 page
Scaling near the upper critical dimensionality in the localization theory
The phenomenon of upper critical dimensionality d_c2 has been studied from
the viewpoint of the scaling concepts. The Thouless number g(L) is not the only
essential variable in scale transformations, because there is the second
parameter connected with the off-diagonal disorder. The investigation of the
resulting two-parameter scaling has revealed two scenarios, and the switching
from one to another scenario determines the upper critical dimensionality. The
first scenario corresponds to the conventional one-parameter scaling and is
characterized by the parameter g(L) invariant under scale transformations when
the system is at the critical point. In the second scenario, the Thouless
number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation
of the Wegner relation s=\nu(d-2) between the critical exponents for
conductivity (s) and for localization radius (\nu), which takes the form
s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the
symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous
version of Mott's argument concerning localization due topological disorder has
been proposed.Comment: PDF, 7 pages, 6 figure
Magnetization driven metal - insulator transition in strongly disordered Ge:Mn magnetic semiconductors
We report on the temperature and field driven metal-insulator transition in
disordered Ge:Mn magnetic semiconductors accompanied by magnetic ordering,
magnetoresistance reaching thousands of percents and suppression of the
extraordinary Hall effect by a magnetic field. Magnetoresistance isotherms are
shown to obey a universal scaling law with a single scaling parameter depending
on temperature and fabrication. We argue that the strong magnetic disorder
leads to localization of charge carriers and is the origin of the unusual
properties of Ge:Mn alloys.Comment: 10 pages, 5 figure
Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?
An analytical realization is suggested for the finite-size scaling algorithm
based on the consideration of auxiliary quasi-1D systems. Comparison of the
obtained analytical results with the results of numerical calculations
indicates that the Anderson transition point is splitted into the band of
critical states. This conclusion is supported by direct numerical evidence
(Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990).
The possibility of restoring the conventional picture still exists but requires
a radical reinterpretetion of the raw numerical data.Comment: PDF, 11 page
Finite-size scaling from self-consistent theory of localization
Accepting validity of self-consistent theory of localization by Vollhardt and
Woelfle, we derive the finite-size scaling procedure used for studies of the
critical behavior in d-dimensional case and based on the use of auxiliary
quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good
agreement with numerical results: it signifies the absence of essential
contradictions with the Vollhardt and Woelfle theory on the level of raw data.
The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of
the correlation length, are explained by the fact that dependence L+L_0 with
L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu}
with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived;
it demonstrates incorrectness of the conventional treatment of data for d=4 and
d=5, but establishes the constructive procedure for such a treatment.
Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with
high precision data by Kramer et a
Gell-Mann - Low Function for QCD in the strong-coupling limit
The Gell-Mann - Low function \beta(g) in QCD (g=g0^2/16\pi^2 where g0 is the
coupling constant in the Lagrangian) is shown to behave in the strong-coupling
region as \beta_\infty g^\alpha with \alpha\approx -13, \beta_\infty\sim 10^5.Comment: 5 pages, PD
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