3,933 research outputs found
Non-Perturbative U(1) Gauge Theory at Finite Temperature
For compact U(1) lattice gauge theory (LGT) we have performed a finite size
scaling analysis on lattices for fixed by
extrapolating spatial volumes of size to . Within the
numerical accuracy of the thus obtained fits we find for , 5 and~6
second order critical exponents, which exhibit no obvious
dependence. The exponents are consistent with 3d Gaussian values, but not with
either first order transitions or the universality class of the 3d XY model. As
the 3d Gaussian fixed point is known to be unstable, the scenario of a yet
unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of
the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure
Block Diagonalization using SRG Flow Equations
By choosing appropriate generators for the Similarity Renormalization Group
(SRG) flow equations, different patterns of decoupling in a Hamiltonian can be
achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent
nucleon-nucleon potentials in momentum space are generated as examples and
compared to analogous low-momentum interactions ("v_lowk").Comment: 4 pages, 9 figures (pdfLaTeX
An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice
It is often assumed that for treating numerical (or experimental) data on
continuous transitions the formal analysis derived from the Renormalization
Group Theory can only be applied over a narrow temperature range, the "critical
region"; outside this region correction terms proliferate rendering attempts to
apply the formalism hopeless. This pessimistic conclusion follows largely from
a choice of scaling variables and scaling expressions which is traditional but
which is very inefficient for data covering wide temperature ranges. An
alternative "extended caling" approach can be made where the choice of scaling
variables and scaling expressions is rationalized in the light of well
established high temperature series expansion developments. We present the
extended scaling approach in detail, and outline the numerical technique used
to study the 3d Ising model. After a discussion of the exact expressions for
the historic 1d Ising spin chain model as an illustration, an exhaustive
analysis of high quality numerical data on the canonical simple cubic lattice
3d Ising model is given. It is shown that in both models, with appropriate
scaling variables and scaling expressions (in which leading correction terms
are taken into account where necessary), critical behavior extends from Tc up
to infinite temperature.Comment: 16 pages, 17 figure
Wither the sliding Luttinger liquid phase in the planar pyrochlore
Using series expansion based on the flow equation method we study the zero
temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the
limit of strong diagonal coupling. Starting from the limit of decoupled crossed
dimers we analyze the evolution of the ground state energy and the elementary
triplet excitations in terms of two coupling constants describing the inter
dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the
fully frustrated inter chain coupling is critical, forcing a dimer phase which
adiabatically connects to the state of isolated dimers. This result is
consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev.
B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding
Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl
Dynamical modelling of luminous and dark matter in 17 Coma early-type galaxies
Dynamical models for 17 Coma early-type galaxies are presented. The galaxy
sample consists of flattened, rotating as well as non-rotating early-types
including cD and S0 galaxies with luminosities between M=-18.79 and M=-22.56.
Kinematical long-slit observations cover at least the major and minor axis and
extend to 1-4 effective radii. Axisymmetric Schwarzschild models are used to
derive stellar mass-to-light ratios and dark halo parameters. In every galaxy
models with a dark matter halo match the data better than models without. The
statistical significance is over 95 percent for 8 galaxies, around 90 percent
for 5 galaxies and for four galaxies it is not significant. For the highly
significant cases systematic deviations between observed and modelled
kinematics are clearly seen; for the remaining galaxies differences are more
statistical in nature. Best-fit models contain 10-50 percent dark matter inside
the half-light radius. The central dark matter density is at least one order of
magnitude lower than the luminous mass density. The central phase-space density
of dark matter is often orders of magnitude lower than in the luminous
component, especially when the halo core radius is large. The orbital system of
the stars along the major-axis is slightly dominated by radial motions. Some
galaxies show tangential anisotropy along the minor-axis, which is correlated
with the minor-axis Gauss-Hermite coefficient H4. Changing the balance between
data-fit and regularisation constraints does not change the reconstructed mass
structure significantly. Model anisotropies tend to strengthen if the weight on
regularisation is reduced, but the general property of a galaxy to be radially
or tangentially anisotropic, respectively, does not change. (abridged)Comment: 31 pages, 34 figures; accepted for publication in MNRA
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
A metal-insulator transition as a quantum glass problem
We discuss a recent mapping of the Anderson-Mott metal-insulator transition
onto a random field magnet problem. The most important new idea introduced is
to describe the metal-insulator transition in terms of an order parameter
expansion rather than in terms of soft modes via a nonlinear sigma model. For
spatial dimensions d>6 a mean field theory gives the exact critical exponents.
In an epsilon expansion about d=6 the critical exponents are identical to those
for a random field Ising model. Dangerous irrelevant quantum fluctuations
modify Wegner's scaling law relating the conductivity exponent to the
correlation or localization length exponent. This invalidates the bound s>2/3
for the conductivity exponent s in d=3. We also argue that activated scaling
might be relevant for describing the AMT in three-dimensional systems.Comment: 10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final
version as publishe
The Wilson Effective K\"ahler Potential For Supersymmetric Nonlinear Sigma Models
Renormalization group methods are used to determine the evolution of the low
energy Wilson effective action for supersymmetric nonlinear sigma models in
four dimensions. For the case of supersymmetric models, the
K\"ahler potential is determined exactly and is shown to exhibit a nontrivial
ultraviolet fixed point in addition to a trivial infrared fixed point. The
strong coupling behavior of the theory suggests the possible existence of
additional relevant operators or nonperturbative degrees of freedom.Comment: 9 pages, LaTeX, 1 eps figur
Fluctuations of the correlation dimension at metal-insulator transitions
We investigate numerically the inverse participation ratio, , of the 3D
Anderson model and of the power-law random banded matrix (PRBM) model at
criticality. We found that the variance of scales with system size
as , being the
correlation dimension and the system dimension. Therefore the concept of a
correlation dimension is well defined in the two models considered. The 3D
Anderson transition and the PRBM transition for (see the text for the
definition of ) are fairly similar with respect to all critical magnitudes
studied.Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Let
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