309 research outputs found
SU(2) Lattice Gauge Theory with Logarithmic Action: Scaling and Universality
We investigate a version of SU(2) lattice gauge theory with a logarithmic
action. The model is found to exhibit confinement, contrary to previous claims
in the literature. Comparing ratios of physical quantities, like
, we find that the model belongs to the same universality
class as the standard SU(2) lattice gauge theory with Wilson action. Like the
positive plaquette model, the model with logarithmic action has a monotonic
-function, without the famous dip exhibited by the Wilson action. Short
distance dislocations affecting the definition of topology are slightly more
suppressed than for the positive plaquette model.Comment: 19 pages. Self-unwrapping compressed postscript fil
Four-quark flux distribution and binding in lattice SU(2)
The full spatial distribution of the color fields of two and four static
quarks is measured in lattice SU(2) field theory at separations up to 1 fm at
beta=2.4. The four-quark case is equivalent to a qbar q qbar q system in SU(2)
and is relevant to meson-meson interactions. By subtracting two-body flux tubes
from the four-quark distribution we isolate the flux contribution connected
with the four-body binding energy. This contribution is further studied using a
model for the binding energies. Lattice sum rules for two and four quarks are
used to verify the results.Comment: 46 pages including 71 eps figures. 3D color figures are available at
www.physics.helsinki.fi/~ppennane/pics
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Critical Exponents of the Superconducting Phase Transition
We study the critical exponents of the superconducting phase transition in
the context of renormalization group theory starting from a dual formulation of
the Ginzburg-Landau theory. The dual formulation describes a loop gas of
Abrikosov flux tubes which proliferate when the critical temperature is
approached from below. In contrast to the Ginzburg-Landau theory, it has a
spontaneously broken global symmetry and possesses an infrared stable fixed
point. The exponents coincide with those of a superfluid with reversed
temperature axis.Comment: Postscript file. For related work see www adress
http://www.physik.fu-berlin.de/kleiner_re.html in our homepage
http://www.physik.fu-berlin.de/kleinert.htm
Renormalons in Effective Field Theories
We investigate the high-order behavior of perturbative matching conditions in
effective field theories. These series are typically badly divergent, and are
not Borel summable due to infrared and ultraviolet renormalons which introduce
ambiguities in defining the sum of the series. We argue that, when treated
consistently, there is no physical significance to these ambiguities. Although
nonperturbative matrix elements and matching conditions are in general
ambiguous, the ambiguity in any physical observable is always higher order in
than the theory has been defined. We discuss the implications for the
recently noticed infrared renormalon in the pole mass of a heavy quark. We show
that a ratio of form factors in exclusive decays (which is related
to the pole mass) is free from renormalon ambiguities regardless of the mass
used as the expansion parameter of HQET. The renormalon ambiguities also cancel
in inclusive heavy hadron decays. Finally, we demonstrate the cancellation of
renormalons in a four-Fermi effective theory obtained by integrating out a
heavy colored scalar.Comment: Minor changes mad
Maximal variance reduction for stochastic propagators with applications to the static quark spectrum
We study a new method -- maximal variance reduction -- for reducing the
variance of stochastic estimators for quark propagators. We find that while
this method is comparable to usual iterative inversion for light-light mesons,
a considerable improvement is achieved for systems containing at least one
infinitely heavy quark. Such systems are needed for heavy quark effective
theory. As an illustration of the effectiveness of the method we present
results for the masses of the ground state and excited states of
mesons and baryons. We compare these results with the experimental
spectra involving quarks.Comment: 31 pages with 7 postscript file
An Extended Variational Principle for the SK Spin-Glass Model
The recent proof by F. Guerra that the Parisi ansatz provides a lower bound
on the free energy of the SK spin-glass model could have been taken as offering
some support to the validity of the purported solution. In this work we present
a broader variational principle, in which the lower bound, as well as the
actual value, are obtained through an optimization procedure for which
ultrametic/hierarchal structures form only a subset of the variational class.
The validity of Parisi's ansatz for the SK model is still in question. The new
variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex
Uniformity transition for ray intensities in random media
This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After N iterations, the intensity is modelled as a sum S of N contributions from different trajectories, each of which is a product of N independent identically distributed random variables xk, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: N=ΛN, for some Λ>1. We investigate the probability distribution of S. We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of S are suppressed as N → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis
Distribution of the color fields around static quarks: Flux tube profiles
We report detailed calculations of the profiles of energy and action
densities in the quark-antiquark string in SU(2) lattice gauge theory.Comment: 40 pages, LSUHE 94-15
Short-range spin glasses and Random Overlap Structures
Properties of Random Overlap Structures (ROSt)'s constructed from the
Edwards-Anderson (EA) Spin Glass model on with periodic boundary
conditions are studied. ROSt's are random matrices whose entries
are the overlaps of spin configurations sampled from the Gibbs measure. Since
the ROSt construction is the same for mean-field models (like the
Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the
setup is a good common ground to study the effect of dimensionality on the
properties of the Gibbs measure. In this spirit, it is shown, using translation
invariance, that the ROSt of the EA model possesses a local stability that is
stronger than stochastic stability, a property known to hold at almost all
temperatures in many spin glass models with Gaussian couplings. This fact is
used to prove stochastic stability for the EA spin glass at all temperatures
and for a wide range of coupling distributions. On the way, a theorem of Newman
and Stein about the pure state decomposition of the EA model is recovered and
extended.Comment: 27 page
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