133 research outputs found
An Infrared Safe perturbative approach to Yang-Mills correlators
We investigate the 2-point correlation functions of Yang-Mills theory in the
Landau gauge by means of a massive extension of the Faddeev-Popov action. This
model is based on some phenomenological arguments and constraints on the
ultraviolet behavior of the theory. We show that the running coupling constant
remains finite at all energy scales (no Landau pole) for and argue that
the relevant parameter of perturbation theory is significantly smaller than 1
at all energies. Perturbative results at low orders are therefore expected to
be satisfactory and we indeed find a very good agreement between 1-loop
correlation functions and the lattice simulations, in 3 and 4 dimensions.
Dimension 2 is shown to play the role of an upper critical dimension, which
explains why the lattice predictions are qualitatively different from those in
higher dimensions.Comment: 16 pages, 7 figures, accepted for publication in PR
Critical behavior of Griffiths ferromagnets
From a heuristic calculation of the leading order essential singularity in
the distribution of Yang-Lee zeroes, we obtain new scaling relations near the
ferromagnetic-Griffiths transition, including the prediction of a discontinuity
on the analogue of the critical isotherm. We show that experimental data for
the magnetization and heat capacity of are
consistent with these predictions, thus supporting its identification as a
Griffiths ferromagnet.Comment: 4 pages, 3 figures, Changed conten
Topological delocalization of two-dimensional massless Dirac fermions
The beta function of a two-dimensional massless Dirac Hamiltonian subject to
a random scalar potential, which e.g., underlies the theoretical description of
graphene, is computed numerically. Although it belongs to, from a symmetry
standpoint, the two-dimensional symplectic class, the beta function
monotonically increases with decreasing . We also provide an argument based
on the spectral flows under twisting boundary conditions, which shows that none
of states of the massless Dirac Hamiltonian can be localized.Comment: 4 pages, 2 figure
Theory of Anomalous Quantum Hall Effects in Graphene
Recent successes in manufacturing of atomically thin graphite samples
(graphene) have stimulated intense experimental and theoretical activity. The
key feature of graphene is the massless Dirac type of low-energy electron
excitations. This gives rise to a number of unusual physical properties of this
system distinguishing it from conventional two-dimensional metals. One of the
most remarkable properties of graphene is the anomalous quantum Hall effect. It
is extremely sensitive to the structure of the system; in particular, it
clearly distinguishes single- and double-layer samples. In spite of the
impressive experimental progress, the theory of quantum Hall effect in graphene
has not been established. This theory is a subject of the present paper. We
demonstrate that the Landau level structure by itself is not sufficient to
determine the form of the quantum Hall effect. The Hall quantization is due to
Anderson localization which, in graphene, is very peculiar and depends strongly
on the character of disorder. It is only a special symmetry of disorder that
may give rise to anomalous quantum Hall effects in graphene. We analyze the
symmetries of disordered single- and double-layer graphene in magnetic field
and identify the conditions for anomalous Hall quantization.Comment: 13 pages (article + supplementary material), 5 figure
A Renormalization-Group approach to the Coulomb Gap
The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.Comment: 16 pages, LaTeX. Diagrams available on request from
[email protected]. Changes to figure 4 and second half of section
Hall plateau diagram for the Hofstadter butterfly energy spectrum
We extensively study the localization and the quantum Hall effect in the
Hofstadter butterfly, which emerges in a two-dimensional electron system with a
weak two-dimensional periodic potential. We numerically calculate the Hall
conductivity and the localization length for finite systems with the disorder
in general magnetic fields, and estimate the energies of the extended levels in
an infinite system. We obtain the Hall plateau diagram on the whole region of
the Hofstadter butterfly, and propose a theory for the evolution of the plateau
structure with increasing disorder. There we show that a subband with the Hall
conductivity has separated bunches of extended levels, at least
for an integer . We also find that the clusters of the subbands with
identical Hall conductivity, which repeatedly appear in the Hofstadter
butterfly, have a similar localization property.Comment: 9 pages, 12 figure
Condensation temperature of interacting Bose gases with and without disorder
The momentum-shell renormalization group (RG) is used to study the
condensation of interacting Bose gases without and with disorder. First of all,
for the homogeneous disorder-free Bose gas the interaction-induced shifts in
the critical temperature and chemical potential are determined up to second
order in the scattering length. The approach does not make use of dimensional
reduction and is thus independent of previous derivations. Secondly, the RG is
used together with the replica method to study the interacting Bose gas with
delta-correlated disorder. The flow equations are derived and found to reduce,
in the high-temperature limit, to the RG equations of the classical
Landau-Ginzburg model with random-exchange defects. The random fixed point is
used to calculate the condensation temperature under the combined influence of
particle interactions and disorder.Comment: 7 pages, 2 figure
Magnetic-Field Dependence of the Localization Length in Anderson Insulators
Using the conventional scaling approach as well as the renormalization group
analysis in dimensions, we calculate the localization length
in the presence of a magnetic field . For the quasi 1D case the
results are consistent with a universal increase of by a numerical
factor when the magnetic field is in the range
\ell\ll{\ell_{\!{_H}}}\alt\xi(0), is the mean free path,
is the magnetic length . However, for
where the magnetic field does cause delocalization there is no
universal relation between and . The effect of spin-orbit
interaction is briefly considered as well.Comment: 4 pages, revtex, no figures; to be published in Europhysics Letter
Two parameter flow of \sigma_{xx}(\omega) - \sigma_{xy}(\omega) for the graphene quantum Hall system in ac regime
Flow diagram of in finite-frequency ()
regime is numerically studied for graphene quantum Hall effect (QHE) system.
The ac flow diagrams turn out to show qualitatively similar behavior as the dc
flow diagrams, which can be understood that the dynamical length scale
determined by the frequency poses a relevant cutoff for the renormalization
flow. Then the two parameter flow is discussed in terms of the dynamical
scaling theory. We also discuss the larger- regime which exhibits
classical flows driven by the raw frequency .Comment: 6 pages, 4 figure
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