8,116 research outputs found
Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory
The pressure of QCD admits at high temperatures a factorization into purely
perturbative contributions from "hard" thermal momenta, and slowly convergent
as well as non-perturbative contributions from "soft" thermal momenta. The
latter can be related to various effective gluon condensates in a dimensionally
reduced effective field theory, and measured there through lattice simulations.
Practical measurements of one of the relevant condensates have suffered,
however, from difficulties in extrapolating convincingly to the continuum
limit. In order to gain insight on this problem, we employ Numerical Stochastic
Perturbation Theory to estimate the problematic condensate up to 4-loop order
in lattice perturbation theory. Our results seem to confirm the presence of
"large" discretization effects, going like , where is the
lattice spacing. For definite conclusions, however, it would be helpful to
repeat the corresponding part of our study with standard lattice perturbation
theory techniques.Comment: 35 pages. v2: minor corrections, published versio
Four-loop pressure of massless O(N) scalar field theory
Inspired by the corresponding problem in QCD, we determine the pressure of
massless O(N) scalar field theory up to order g^6 in the weak-coupling
expansion, where g^2 denotes the quartic coupling constant. This necessitates
the computation of all 4-loop vacuum graphs at a finite temperature: by making
use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate
that this task is manageable at least if one restricts to computing the
logarithmic terms analytically, while handling the ``constant'' 4-loop
contributions numerically. We also inspect the numerical convergence of the
weak-coupling expansion after the inclusion of the new terms. Finally, we point
out that while the present computation introduces strategies that should be
helpful for the full 4-loop computation on the QCD-side, it also highlights the
need to develop novel computational techniques, in order to be able to complete
this formidable task in a systematic fashion.Comment: 34 page
Renormalization of infrared contributions to the QCD pressure
Thanks to dimensional reduction, the infrared contributions to the QCD
pressure can be obtained from two different three-dimensional effective field
theories, called the Electrostatic QCD (Yang-Mills plus adjoint Higgs) and the
Magnetostatic QCD (pure Yang-Mills theory). Lattice measurements have been
carried out within these theories, but a proper interpretation of the results
requires renormalization, and in some cases also improvement, i.e. the removal
of terms of O(a) or O(a^2). We discuss how these computations can be
implemented and carried out up to 4-loop level with the help of Numerical
Stochastic Perturbation Theory.Comment: 7 pages, 4 figures, talk presented at Lattice 2006 (High temperature
and density
The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure
Using Numerical Stochastic Perturbation Theory within three-dimensional pure
SU(3) gauge theory, we estimate the last unknown renormalization constant that
is needed for converting the vacuum energy density of this model from lattice
regularization to the MSbar scheme. Making use of a previous non-perturbative
lattice measurement of the plaquette expectation value in three dimensions,
this allows us to approximate the first non-perturbative coefficient that
appears in the weak-coupling expansion of hot QCD pressure.Comment: 16 pages. v2: published versio
3-d lattice SU(3) free energy to four loops
We report on the perturbative computation of the 3d lattice Yang-Mills free
energy to four loops by means of Numerical Stochastic Perturbation Theory. The
known first and second orders have been correctly reproduced; the third and
fourth order coefficients are new results and the known logarithmic IR
divergence in the fourth order has been correctly identified. Progress is being
made in switching to the gluon mass IR regularization and the related inclusion
of the Faddeev-Popov determinant.Comment: Lattice2004(non-zero), 3 pages, 2 figure
3-d Lattice QCD Free Energy to Four Loops
We compute the expansion of the 3-d Lattice QCD free energy to four loop
order by means of Numerical Stochastic Perturbation Theory. The first and
second order are already known and are correctly reproduced. The third and
fourth order coefficients are new results. The known logarithmic divergence in
the fourth order is correctly identified. We comment on the relevance of our
computation in the context of dimensionally reduced finite temperature QCD.Comment: 8 pages, 3 figures, latex typeset with JHEP3.cl
Fermi-surface collapse and dynamical scaling near a quantum critical point
Quantum criticality arises when a macroscopic phase of matter undergoes a
continuous transformation at zero temperature. While the collective
fluctuations at quantum-critical points are being increasingly recognized as
playing an important role in a wide range of quantum materials, the nature of
the underlying quantum-critical excitations remains poorly understood. Here we
report in-depth measurements of the Hall effect in the heavy-fermion metal
YbRh2Si2, a prototypical system for quantum criticality. We isolate a rapid
crossover of the isothermal Hall coefficient clearly connected to the
quantum-critical point from a smooth background contribution; the latter exists
away from the quantum-critical point and is detectable through our studies only
over a wide range of magnetic field. Importantly, the width of the critical
crossover is proportional to temperature, which violates the predictions of
conventional theory and is instead consistent with an energy over temperature,
E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our
results provide evidence that the quantum-dynamical scaling and a critical
Kondo breakdown simultaneously operate in the same material. Correspondingly,
we infer that macroscopic scale-invariant fluctuations emerge from the
microscopic many-body excitations associated with a collapsing Fermi-surface.
This insight is expected to be relevant to the unconventional
finite-temperature behavior in a broad range of strongly correlated quantum
systems.Comment: 5 pages, plus supporting materia
Magnetic Flares on Asymptotic Giant Branch Stars
We investigate the consequences of magnetic flares on the surface of
asymptotic giant branch (AGB) and similar stars. In contrast to the solar wind,
in the winds of AGB stars the gas cooling time is much shorter than the outflow
time. As a result, we predict that energetic flaring will not inhibit, and may
even enhance, dust formation around AGB stars. If magnetic flares do occur
around such stars, we expect some AGB stars to exhibit X-ray emission; indeed
certain systems including AGB stars, such as Mira, have been detected in
X-rays. However, in these cases, it is difficult to distinguish between
potential AGB star X-ray emission and, e.g., X-ray emission from the vicinity
of a binary companion. Analysis of an archival ROSAT X-ray spectrum of the Mira
system suggests an intrinsic X-ray luminosity 2x10^{29} erg/sec and temperature
10^7 K. These modeling results suggest that magnetic activity, either on the
AGB star (Mira A) or on its nearby companion (Mira B), is the source of the
X-rays, but do not rule out the possibility that the X-rays are generated by an
accretion disk around Mira B.Comment: ApJ, Accepted; revised version of astro-ph/020923
Towards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure
Thanks to dimensional reduction, the contributions to the hot QCD pressure
coming from so-called soft modes can be studied via an effective
three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields
plus an adjoint Higgs scalar). The poor convergence of the perturbative series
within EQCD suggests to perform lattice measurements of some of the associated
gluon condensates. These turn out, however, to be plagued by large
discretization artifacts. We discuss how Numerical Stochastic Perturbation
Theory can be exploited to determine the full lattice spacing dependence of one
of these condensates up to 4-loop order, and sharpen our tools on a concrete
2-loop example.Comment: Presented at 25th International Symposium on Lattice Field Theory,
Regensburg, Germany, 30 Jul - 4 Aug 2007, 7 page
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