424 research outputs found
Non--perturbative tests of the fixed point action for SU(3) gauge theory
In this paper (the second of a series) we extend our calculation of a
classical fixed point action for lattice pure gauge theory to include
gauge configurations with large fluctuations. The action is parameterized in
terms of closed loops of link variables. We construct a few-parameter
approximation to the classical FP action which is valid for short correlation
lengths. We perform a scaling test of the action by computing the quantity where the string tension is measured from the
torelon mass . We measure on lattices of fixed physical
volume and varying lattice spacing (which we define through the
deconfinement temperature). While the Wilson action shows scaling violations of
about ten per cent, the approximate fixed point action scales within the
statistical errors for . Similar behaviour is found for
the potential measured in a fixed physical volume.Comment: 28 pages (latex) + 11 figures (Postscript), uuencode
First results from a parametrized Fixed-Point QCD action
We have constructed a new fermion action which is an approximation to the
(chirally symmetric) Fixed-Point action, containing the full Clifford algebra
with couplings inside a hypercube and paths built from renormalization group
inspired fat links. We present an exploratory study of the light hadron
spectrum and the energy-momentum dispersion relation.Comment: Lattice2001(improvement), 3 pages, based on a talk by S.H; reference
update
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
Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
We report on an ongoing project to parametrize the Fixed-Point Dirac operator
for massless quarks, using a very general construction which has arbitrarily
many fermion offsets and gauge paths, the complete Clifford algebra and
satisfies all required symmetries. Optimizing a specific construction with
hypercubic fermion offsets, we present some preliminary results.Comment: Lattice 2000 (Improvement), 9 pages, based on a talk by K.H. and a
poster by T.J. References adde
Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
We investigate the cutoff effects in 2-d lattice O(N) models for a variety of
lattice actions, and we identify a class of very simple actions for which the
lattice artifacts are extremely small. One action agrees with the standard
action, except that it constrains neighboring spins to a maximal relative angle
delta. We fix delta by demanding that a particular value of the step scaling
function agrees with its continuum result already on a rather coarse lattice.
Remarkably, the cutoff effects of the entire step scaling function are then
reduced to the per mille level. This also applies to the theta-vacuum effects
of the step scaling function in the 2-d O(3) model. The cutoff effects of other
physical observables including the renormalized coupling and the mass in the
isotensor channel are also reduced drastically. Another choice, the mixed
action, which combines the standard quadratic with an appropriately tuned large
quartic term, also has extremely small cutoff effects. The size of cutoff
effects is also investigated analytically in 1-d and at N = infinity in 2-d.Comment: 39 pages, 18 figure
The construction of generalized Dirac operators on the lattice
We discuss the steps to construct Dirac operators which have arbitrary
fermion offsets, gauge paths, a general structure in Dirac space and satisfy
the basic symmetries (gauge symmetry, hermiticity condition, charge
conjugation, hypercubic rotations and reflections) on the lattice. We give an
extensive set of examples and offer help to add further structures.Comment: 19 pages, latex, maple code attache
The index theorem in QCD with a finite cut-off
The fixed point Dirac operator on the lattice has exact chiral zero modes on
topologically non-trivial gauge field configurations independently whether
these configurations are smooth, or coarse. The relation ,
where is the number of left (right)-handed zero modes and
is the fixed point topological charge holds not only in the continuum
limit, but also at finite cut-off values. The fixed point action, which is
determined by classical equations, is local, has no doublers and complies with
the no-go theorems by being chirally non-symmetric. The index theorem is
reproduced exactly, nevertheless. In addition, the fixed point Dirac operator
has no small real eigenvalues except those at zero, i.e. there are no
'exceptional configurations'.Comment: 9 pages, 1 figure. Minor clarifying changes are made and new
references adde
Logarithmic corrections to O(a(2)) lattice artifacts
We compute logarithmic corrections to the O(a(2)) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form a(2)vertical bar In(a(2))vertical bar(n/(n-2)). We also compute the next-to-leading corrections and show that for the case n = 3 the resulting expressions describe well the lattice artifacts in the step scaling function, which are in a large range of the cutoff apparently of the form O(a). An analogous computation should, if technically possible, accompany ally precision measurements in lattice QCD. (C) 2009 Elsevier B.V. All rights reserved
Lattice regularization and symmetries
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice. © SISSA 2006
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