631 research outputs found
Perfect topological charge for asymptotically free theories
The classical equations of motion of the perfect lattice action in
asymptotically free spin and gauge models possess scale invariant
instanton solutions. This property allows the definition of a topological
charge on the lattice which is perfect in the sense that no topological defects
exist. The basic construction is illustrated in the O(3) non--linear
--model and the topological susceptibility is measured to high
precision in the range of correlation lengths . Our results
strongly suggest that the topological susceptibility is not a physical quantity
in this model.Comment: Contribution to Lattice'94, 3 pages PostScript, uuencoded compresse
Setting the scale for the Luescher-Weisz action
We study the quark-antiquark potential of quenched SU(3) lattice gauge theory
with the Luescher-Weisz action. After blocking the gauge fields with the
recently proposed hypercubic transformation we compute the Sommer parameter,
extract the lattice spacing a and set the scale at 6 different values of the
gauge coupling in a range from a = 0.084 fm to 0.136 fm.Comment: Remarks and references added, to appear in Phys. Rev.
Towards Weyl fermions on the lattice without artefacts
In spite of the breakthrough in non-perturbative chiral gauge theories during
the last decade, the present formulation has stubborn artefacts. Independently
of the fermion representation one is confronted with unwanted CP violation and
infinitely many undetermined weight factors. Renormalization group identifies
the culprit. We demonstrate the procedure on Weyl fermions in a real
representation
The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
The correlation length of the square-lattice spin-1/2 Heisenberg
antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime.
Our novel approach combines a very efficient loop cluster algorithm --
operating directly in the Euclidean time continuum -- with finite-size scaling.
This enables us to probe correlation lengths up to
lattice spacings -- more than three orders of magnitude larger than any
previous study. We resolve a conundrum concerning the applicability of
asymptotic-scaling formulae to experimentally- and numerically-determined
correlation lengths, and arrive at a very precise determination of the
low-energy observables. Our results have direct implications for the
zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor
modifications for final submission to Physical Review Letters. (accepted by
PRL
Ginsparg-Wilson Relation and Ultralocality
It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in four dimensions that is: (a)
ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding
kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation),
(d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change
A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model
A scaling hypothesis for the n-particle spectral densities of the O(3)
nonlinear sigma-model is described. It states that for large particle numbers
the n-particle spectral densities are ``self-similar'' in being basically
rescaled copies of a universal shape function. This can be viewed as a
2-dimensional, but non-perturbative analogue of the KNO scaling in QCD.
Promoted to a working hypothesis, it allows one to compute the two point
functions at ``all'' energy or length scales. In addition, the values of two
non-perturbative constants (needed for a parameter-free matching of the
perturbative and the non-perturbative regime) are determined exactly.Comment: 9 Pages, Latex, 3 Postscript Figure
Testing the self-duality of topological lumps in SU(3) lattice gauge theory
We discuss a simple formula which connects the field-strength tensor to a
spectral sum over certain quadratic forms of the eigenvectors of the lattice
Dirac operator. We analyze these terms for the near zero-modes and find that
they give rise to contributions which are essentially either self-dual or anti
self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more
dominated by quantum fluctuations and are less (anti) self-dual. In the high
temperature phase of QCD we find considerably reduced (anti) self-duality for
the modes near the edge of the spectral gap.Comment: Remarks added, to appear in Phys. Rev. Let
Improving lattice perturbation theory
Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at the `tadpole renormalized' coupling to be compared to the non-perturbative numerical value Comment: Plain TeX, 8 page
Tests of the continuum limit for the Principal Chiral Model and the prediction for \L_\MS
We investigate the continuum limit in Principal Chiral Models
concentrating in detail on the model and its covering group
SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the
prediction of Hollowood of m/\L_\MS = 3.8716. We use the finite-size scaling
method of L\"uscher et al. to deduce m/\L_\MS and find that for the
model the computed result of m/\L_\MS \sim 14 is in strong disagreement with
theory but that a similar analysis of the SU(2)xSU(2) yields excellent
agreement with theory. We conjecture that for violations of the
finite-size scaling assumption are severe forthe values of the correlation
length, , investigated and that our attempts to extrapolate the results to
zero lattice spacing, although plausible, are erroneous. Conversely, the
finite-size scaling violations in the SU(2)xSU(2) simulation are consistent
with perturbation theory and the computed function agrees well with the
3-loop approximation for couplings evaluated at scales , where
is measured in units of the lattice spacing, . We conjecture that
lattice vortex artifacts in the model are responsible for delaying the
onset of the continuum limit until much larger correlation lengths are achieved
notwithstanding the apparent onset of scaling. Results for the mass spectrum
for SO(N) m, N=8,10 are given whose comparison with theory gives plausible
support to our ideas.Comment: 27 pages , 1 Postscript-file, uuencode
Ginsparg-Wilson relation and the overlap formula
The fermionic determinant of a lattice Dirac operator that obeys the
Ginsparg-Wilson relation factorizes into two factors that are complex conjugate
of each other. Each factor is naturally associated with a single chiral fermion
and can be realized as a overlap of two many body vacua.Comment: 4 pages, plain tex, no figure
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