145 research outputs found
SU(2) lattice gluon propagators at finite temperatures in the deep infrared region and Gribov copy effects
We study numerically the SU(2) Landau gauge transverse and longitudinal gluon
propagators at non-zero temperatures T both in confinement and deconfinement
phases. The special attention is paid to the Gribov copy effects in the
IR-region. Applying powerful gauge fixing algorithm we find that the Gribov
copy effects for the transverse propagator D_T(p) are very strong in the
infrared, while the longitudinal propagator D_L(p) shows very weak (if any)
Gribov copy dependence. The value D_T(0) tends to decrease with growing lattice
size; however, D_T(0) is non-zero in the infinite volume limit, in disagreement
with the suggestion made in [1]. We show that in the infrared region D_T(p) is
not consistent with the pole-type formula not only in the deconfinement phase
but also for T < T_c. We introduce new definition of the magnetic infrared mass
scale ('magnetic screening mass') m_M. The electric mass m_E has been
determined from the momentum space longitudinal gluon propagator. We study also
the (finite) volume and temperature dependence of the propagators as well as
discretization errors.Comment: 11 pages, 14 figures, 3 tables. Few minor change
Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory
Green's functions are a central element in the attempt to understand
non-perturbative phenomena in Yang-Mills theory. Besides the propagators,
3-point Green's functions play a significant role, since they permit access to
the running coupling constant and are an important input in functional methods.
Here we present numerical results for the two non-vanishing 3-point Green's
functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e.
the three-gluon vertex and the ghost-gluon vertex, considering various
kinematical regimes. In this exploratory investigation the lattice volumes are
limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for
the gluon and the ghost propagators, as well as for the eigenvalue spectrum of
the Faddeev-Popov operator. Finally, we compare two different numerical methods
for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source
and the plane-wave-source methods.Comment: 18 pages, 12 figures, 3 table
The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N)
Yang-Mills theories in the d-dimensional case. We find a qualitatively
different behavior for d=3,4 w.r.t. d=2. In particular, considering any
(sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost
propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the
infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition
\sigma(p^2) 0) can be satisfied only if D(0) = 0. On the
contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results
are obtained by evaluating G(p^2) explicitly at one loop, using fitting forms
for D(p^2) that describe well the numerical data of D(p^2) in d=2,3,4 in the
SU(2) case. These evaluations also show that, if one considers the coupling
constant g^2 as a free parameter, G(p^2) admits a one-parameter family of
behaviors (labelled by g^2), in agreement with Boucaud et al. In this case the
condition sigma(0) <= 1 implies g^2 <= g^2_c, where g^2_c is a 'critical'
value. Moreover, a free-like G(p^2) in the infrared limit is obtained for any
value of g^2 < g^2_c, while for g^2 = g^2_c one finds an infrared-enhanced
G(p^2). Finally, we analyze the Dyson-Schwinger equation (DSE) for sigma(p^2)
and show that, for infrared-finite ghost-gluon vertices, one can bound
sigma(p^2). Using these bounds we find again that only in the d=2 case does one
need to impose D(0) = 0 in order to satisfy the no-pole condition. The d=2
result is also supported by an analysis of the DSE using a spectral
representation for G(p^2). Thus, if the no-pole condition is imposed, solving
the d=2 DSE cannot lead to a massive behavior for D(p^2). These results apply
to any Gribov copy inside the so-called first Gribov horizon, i.e. the 2d
result D(0) = 0 is not affected by Gribov noise. These findings are also in
agreement with lattice data.Comment: 40 pages, 2 .eps figure
SU(2) Landau gluon propagator on a 140^3 lattice
We present a numerical study of the gluon propagator in lattice Landau gauge
for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2,
5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V
we observe a decreasing gluon propagator for momenta smaller than p_{dec} =
350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem
to indicate an infra-red critical exponent kappa slightly above 0.6, in
agreement with recent analytic results.Comment: 5 pages with 2 figures and 3 tables; added a paragraph on
discretization effect
Renormalization-group Calculation of Color-Coulomb Potential
We report here on the application of the perturbative renormalization-group
to the Coulomb gauge in QCD. We use it to determine the high-momentum
asymptotic form of the instantaneous color-Coulomb potential and
of the vacuum polarization . These quantities are
renormalization-group invariants, in the sense that they are independent of the
renormalization scheme. A scheme-independent definition of the running coupling
constant is provided by , and of , where , and
is a finite QCD mass scale. We also show how to calculate the
coefficients in the expansion of the invariant -function , where all coefficients are scheme-independent.Comment: 24 pages, 1 figure, TeX file. Minor modifications, incorporating
referee's suggestion
Infrared behavior of the gluon propagator in lattice Landau gauge: the three-dimensional case
We evaluate numerically the three-momentum-space gluon propagator in the
lattice Landau gauge, for three-dimensional pure-SU(2) lattice gauge theory
with periodic boundary conditions. Simulations are done for nine different
values of the coupling , from (strong coupling) to (in the scaling region), and for lattice sizes up to . In the
limit of large lattice volume we observe, in all cases, a gluon propagator
decreasing for momenta smaller than a constant value . From our data
we estimate MeV. The result of a gluon propagator
decreasing in the infrared limit has a straightforward interpretation as
resulting from the proximity of the so-called first Gribov horizon in the
infrared directions.Comment: 14 pages, BI-TP 99/03 preprint, correction in the Acknowledgments
section. To appear in Phys.Rev.
Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
We show that the application of a novel gauge invariant truncation scheme to
the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared
finite gluon propagator and a divergent ghost propagator, in qualitative
agreement with recent lattice data.Comment: 9 pages, 2 figures; v3: typos corrected; v2: discussion on numerical
results expanded, considerations about the Kugo-Ojima confinement criterion
adde
Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory
For SU(2) lattice gauge theory we study numerically the infrared behavior of
the Landau gauge ghost and gluon propagators with the special accent on the
Gribov copy dependence. Applying a very efficient gauge fixing procedure and
generating up to 80 gauge copies we find that the Gribov copy effect for both
propagators is essential in the infrared. In particular, our best copy dressing
function of the ghost propagator approaches a plateau in the infrared, while
for the random first copy it still grows. Our best copy zero-momentum gluon
propagator shows a tendency to decrease with growing lattice size which
excludes singular solutions. Our results look compatible with the so-called
decoupling solution with a non-singular gluon propagator. However, we do not
yet consider the Gribov copy problem to be finally resolved.Comment: 9 pages, 9 figure
Canonical Transformations and Renormalization Group Invariance in the presence of Non-trivial Backgrounds
We show that for a SU(N) Yang-Mills theory the classical background-quantum
splitting is non-trivially deformed at the quantum level by a canonical
transformation with respect to the Batalin-Vilkovisky bracket associated with
the Slavnov-Taylor identity of the theory. This canonical transformation acts
on all the fields (including the ghosts) and antifields; it uniquely fixes the
dependence on the background field of all the one-particle irreducible Green's
functions of the theory at hand. The approach is valid both at the perturbative
and non-perturbative level, being based solely on symmetry requirements. As a
practical application, we derive the renormalization group equation in the
presence of a generic background and apply it in the case of a SU(2) instanton.
Finally, we explicitly calculate the one-loop deformation of the
background-quantum splitting in lowest order in the instanton background.Comment: 24 pages, 1 figur
The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-
We simulate the improved three-dimensional two-component phi^4 model on the
simple cubic lattice in the low and the high temperature phase for reduced
temperatures down to |T-T_c|/T_c \approx 0.0017 on lattices of a size up to
350^3. Our new results for the internal energy and the specific heat are
combined with the accurate estimates of beta_c and data for the internal energy
and the specific heat at \beta_c recently obtained in cond-mat/0605083. We find
R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5), where alpha is the critical exponent
of the specific heat and A_{\pm} is the amplitude of the specific heat in the
high and the low temperature phase, respectively.Comment: 14 pages, 4 figure
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