19,160 research outputs found
Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom
Recent progress in understanding the emergence of confinement and other
nonperturbative effects in the strong interaction vacuum is reviewed. Special
emphasis is placed on the role of different types of collective infrared
gluonic degrees of freedom in this respect. After a survey of complementary
approaches, models of the QCD vacuum based on center vortices, Abelian magnetic
monopoles and topological charge lumps such as instantons, merons and calorons
are examined. Both the physical mechanisms governing these models as well as
recent lattice studies of the respective degrees of freedom are reviewed.Comment: 15 pages (14 if you use the original espcrc2.sty instead of the
hypertex-compatible local version), 4 figures containing 7 postscript files,
talk presented at Lattice2004(plenary), Fermilab, June 21-26, 2004. Replaced
version contains an additional reference and a corresponding commen
Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
Various lattice geometries and boundaries are used to investigate
valence-bond-solid (VBS) ordering in the ground state of an S=1/2
square-lattice quantum spin model---the J-Q model, in which 4- or 6-spin
interactions Q are added to the Heisenberg exchange J. Ground state results for
finite systems (with up to thousands of spins) are obtained using a projector
QMC method. Great care has to be taken when extrapolating the order parameter
to infinite size, in particular in cylinder geometry. Even though strong 2D VBS
order exists and is established clearly with increasing system size on L*L
lattices (or Lx* Ly lattices with a fixed Lx/Ly), only short-range VBS
correlations are observed on long cylinders (when Lx -> infinity at fixed Ly).
The correlation length increases with Ly, until long-range order sets in at a
"critical" Ly. This width is large even when the 2D order is strong, e.g, for a
system where the order parameter is 70% of the largest possible value, Ly=8 is
required for ordering. Correlation functions for small L*L lattices can also be
misleading. For a 20%-ordered system results for L up to 20 appear to
extrapolate to a vanishing order parameter, while for larger L the behavior
crosses over and extrapolates to a non-zero value (with exponentially small
finite size corrections). The VBS order also exhibits interesting edge effects
related to emergent U(1) symmetry, which, if not considered properly, can lead
to wrong conclusions for the thermodynamic limit. The finite-size behavior for
small L*L lattices and long cylinders is similar to that predicted for a Z2
spin liquid. The results raise concerns about recent works claiming Z2 spin
liquid ground states in frustrated 2D systems, in particular, the Heisenberg
model with nearest and next-nearest-neighbor couplings. VBS state in this
system cannot be ruled out.Comment: 26 pages, 28 figures. v2: final, published versio
Can a stationary Bianchi black brane have momentum along the direction with no translational symmetry?
Bianchi black branes (black brane solutions with homogeneous but anisotropic
horizons classified by the Bianchi type) provide a simple holographic setting
with lattice structures taken into account. In the case of holographic
superconductor, we have a persistent current with lattices. Accordingly, we
expect that in the dual gravity side, a black brane should carry some momentum
along a direction of lattice structure, where translational invariance is
broken. Motivated by this expectation, we consider whether---and if possible,
in what circumstances---a Bianchi black brane can have momentum along a
direction of no-translational invariance. First, we show that this {\it cannot}
be the case for a certain class of stationary Bianchi black brane solutions in
the Einstein-Maxwell-dilation theory. Then we also show that this {\it can} be
the case for some Bianchi VII black branes by numerically constructing such
a solution in the Einstein-Maxwell theory with an additional vector field
having a source term. The horizon of this solution admits a translational
invariance on the horizon and conveys momentum (and is "rotating" when
compactified). However this translational invariance is broken just outside the
horizon. This indicates the existence of a black brane solution which is
regular but non-analytic at the horizon, thereby evading the black hole
rigidity theorem.Comment: 24 pages, 8 figures. v2: section 4 clarified, one more numerical
solution adde
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model
We study a percolation problem on a substrate formed by two-dimensional XY
spin configurations, using Monte Carlo methods. For a given spin configuration
we construct percolation clusters by randomly choosing a direction in the
spin vector space, and then placing a percolation bond between nearest-neighbor
sites and with probability ,
where governs the percolation process. A line of percolation thresholds
is found in the low-temperature range , where
is the XY coupling strength. Analysis of the correlation function , defined as the probability that two sites separated by a distance
belong to the same percolation cluster, yields algebraic decay for , and the associated critical exponent depends on and .
Along the threshold line , the scaling dimension for is,
within numerical uncertainties, equal to . On this basis, we conjecture
that the percolation transition along the line is of the
Berezinskii-Kosterlitz-Thouless type.Comment: 23 pages, 14 figure
Supersonic crack propagation in a class of lattice models of Mode III brittle fracture
We study a lattice model for mode III crack propagation in brittle materials
in a stripe geometry at constant applied stretching. Stiffening of the material
at large deformation produces supersonic crack propagation. For large
stretching the propagation is guided by well developed soliton waves. For low
stretching, the crack-tip velocity has a universal dependence on stretching
that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure
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