55 research outputs found
Universality, Scaling and Topology with a Modified Lattice Action
We examined the effect of a complete suppression of a lattice artifact, the
negative plaquettes, on physical quantities, such as the critical temperature,
the string tension, the topological charge, glueball masses, and their ratios.Comment: 3 pages, self unpacking uuencoded PostScript file, contribution to
conference LATTICE '9
Scaling in the Positive Plaquette Model and Universality in SU(2) Lattice Gauge Theory
We investigate universality, scaling, the beta-function and the topological
charge in the positive plaquette model for SU(2) lattice gauge theory.
Comparing physical quantities, like the critical temperature, the string
tension, glueball masses, and their ratios, we explore the effect of a complete
suppression of a certain lattice artifact, namely the negative plaquettes, for
SU(2) lattice gauge theory. Our result is that this modification does not
change the continuum limit, i.e., the universality class. The positive
plaquette model and the standard Wilson formulation describe the same physical
situation. The approach to the continuum limit given by the beta-function in
terms of the bare lattice coupling, however, is rather different: the
beta-function of the positive plaquette model does not show a dip like the
model with standard Wilson action.Comment: 35 pages, preprint numbers FSU-SCRI-94-71 and HU Berlin-IEP-94/1
Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions
We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge
theories, by simulating lattice theories with a Wilson plaquette action. We
find that there is a strong-to-weak coupling cross-over in the lattice theory
that appears to become a third-order phase transition at N=oo, in a manner that
is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo)
lattice gauge theory. There is also evidence for a second order transition at
N=oo at approximately the same coupling, which is connected with centre
monopoles (instantons) and so analogues to the first order bulk transition that
occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice
spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a
sequence of (apparently) first-order ZN symmetry breaking transitions
associated with each of the tori (ordered by size). We discuss how these
transitions can be understood in terms of a sequence of deconfining transitions
on ever-more dimensionally reduced gauge theories.We investigate whether the
trace of the Wilson loop has a non-analyticity in the coupling at some critical
area, but find no evidence for this although, just as in D=1+1,the eigenvalue
density of a Wilson loop forms a gap at N=oo for a critical trace. The physical
implications of this are unclear.The gap formation is a special case of a
remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1
and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue
spectra are nearly identical.This holds for finite as well as infinite N;
irrespective of the Wilson loop size in lattice units; and for Polyakov as well
as Wilson loops.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new
results on non-analyticities and eigenvalue spectra of Wilson loops. This
version to be submitted for publicatio
Universality of the gauge-ball spectrum of the four-dimensional pure U(1) gauge theory
We continue numerical studies of the spectrum of the pure U(1) lattice gauge
theory in the confinement phase, initiated in our previous work. Using the
extended Wilson action we address the question of universality of the phase
transition line in the () plane between the confinement and the
Coulomb phases. Our present results at for the gauge-ball
spectrum are fully consistent with the previous results obtained at . Again, two different correlation length exponents,
and , are obtained in different channels. We also confirm
the stability of the values of these exponents with respect to the variation of
the distance from the critical point at which they are determined. These
results further demonstrate universal critical behaviour of the model at least
up to correlation lengths of 4 lattice spacings when the phase transition is
approached in some interval at .Comment: 16 page
Gribov Copies in the Maximally Abelian Gauge and Confinement
We fix lattice gauge fields to the Maximally Abelian gauge in both
three and four dimensions. We extract the corresponding fields and
monopole current densities and calculate separately the confining string
tensions arising from these fields and monopole `condensates'. We
generate multiple Gribov copies and study how the fields and monopole
distributions vary between these different copies. As expected, we find
substantial variations in the number of monopoles, their locations and in the
values of the field strengths. The string tensions extracted from
`extreme' Gribov copies also differ but this difference appears to be no more
than about 20\%. We also directly compare the fields of different Gribov
copies. We find that on the distance scales relevant to confinement the
and monopole fluxes that disorder Wilson loops are highly correlated between
these different Gribov copies. All this suggests that while there is indeed a
Gribov copy problem the resulting ambiguity is, in this gauge and for the study
of confinement, of limited importance.Comment: 31 pages LaTeX plus 5 PostScript figures. Uses epsf.sty.
Self-unpacking, uuencoded tar-compressed fil
Topological Structure of the SU(3) Vacuum
We investigate the topological structure of the vacuum in SU(3) lattice gauge
theory. We use under-relaxed cooling to remove the high-frequency fluctuations
and a variety of "filters" to identify the topological charges in the resulting
smoothened field configurations. We find a densely packed vacuum with an
average instanton size, in the continuum limit, of about 0.5 fm. The density at
large sizes decreases as a large inverse power of the size. At small sizes we
see some sign of a trend towards the asymptotic perturbative behaviour. We find
that an interesting polarisation phenomenon occurs: the large topological
charges tend to have, on the average, the same sign and are over-screened by
the smaller charges which tend to have, again on the average, the opposite sign
to the larger instantons. We also calculate the topological susceptibility for
which we obtain a continuum value of about 187 MeV. We perform the calculations
for various volumes, lattice spacings and numbers of cooling sweeps, so as to
obtain some control over the associated systematic errors. The coupling range
is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to
32x32x32x64.Comment: LaTeX. Self-unpacking, uuencoded tar-compressed fil
On the glueball spectrum in O(a)-improved lattice QCD
We calculate the light `glueball' mass spectrum in N_f=2 lattice QCD using a
fermion action that is non-perturbatively O(a) improved. We work at lattice
spacings a ~0.1 fm and with quark masses that range down to about half the
strange quark mass. We find the statistical errors to be moderate and under
control on relatively small ensembles. We compare our mass spectrum to that of
quenched QCD at the same value of a. Whilst the tensor mass is the same (within
errors), the scalar mass is significantly smaller in the dynamical lattice
theory, by a factor of ~(0.84 +/- 0.03). We discuss what the observed m_q
dependence of this suppression tells us about the dynamics of glueballs in QCD.
We also calculate the masses of flux tubes that wind around the spatial torus,
and extract the string tension from these. As we decrease the quark mass we see
a small but growing vacuum expectation value for the corresponding flux tube
operators. This provides clear evidence for `string breaking' and for the
(expected) breaking of the associated gauge centre symmetry by sea quarks.Comment: 33pp LaTeX. Version to appear in Phys. Rev.
On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories
We calculate the energy spectrum of a k=2 flux tube that is closed around a
spatial torus, as a function of its length l. We do so for SU(4) and SU(5)
gauge theories in 2 space dimensions. We find that to a very good approximation
the eigenstates belong to the irreducible representations of the SU(N) group
rather than just to its center, Z_N. We obtain convincing evidence that the
low-lying states are, for l not too small, very close to those of the
Nambu-Goto free string theory (in flat space-time). The correction terms appear
to be typically of O(1) in appropriate units, much as one would expect if the
bosonic string model were an effective string theory for the dynamics of these
flux tubes. This is in marked contrast to the case of fundamental flux tubes
where such corrections have been found to be unnaturally small. Moreover we
find that these corrections appear to be particularly small when the `phonons'
along the string have the same momentum, and large when their momentum is
opposite. This provides information about the detailed nature of the
interactions in the effective string theory. We have searched for, but not
found, extra states that would arise from the excitation of the massive modes
presumably associated with the non-trivial structure of the flux tube.Comment: 37 pages, 16 figures, minor changes to text and figure
The scalar and tensor glueballs in the valence approximation
We evaluate the infinite volume, continuum limit of and
glueball masses in the valence approximation. We find ~MeV and ~MeV, consistent with the interpretation
of as the lightest scalar glueball.Comment: (talk presented by A. Vaccarino at Lattice 93) 3 pages of PostScript
in uufiles compressed form. IBM-HET-94-
Cooling and the SU(2) Instanton Vaccuum
We present results of an investigation into the nature of instantons in
4-dimensional pure gauge lattice \ obtained from configurations which
have been cooled using an under-relaxed cooling algorithm. We discuss ways of
calibrating the cooling and the effects of different degrees of cooling, and
compare our data for the shapes, sizes and locations of instantons with
continuum results. In this paper we extend the ideas and techniques developed
by us for use in , and compare the results with those obtained by other
groups.Comment: 22 pages, LaTeX, uuencoded compressed tarfile of figures sent
separately. Full (compressed) postscript version (118k)available from
ftp://rock.helsinki.fi/pub/preprints/tft/Year1995/HU-TFT-95-21/paper.ps.
- …