7,388 research outputs found
The analysis of Polyakov loop and spin correlators in finite volumes
We derive an analytic expression for point to point correlation functions of
the Polyakov loop based on the transfer matrix formalism. The contributions
from the eigenvalues of the transfer matrix including and beyond the mass gap
are investigated both for the Ising model and in finite temperature
gauge theory. We find that the leading matrix element shows similar
scaling properties in both models. Just above the critical point we obtain for
a Debye screening mass , independent of the volume.
Sorry, figures are not included and can be sent by ordinary mail.Comment: TALK GIVEN AT THE LATTICE '93 INTERNATIONAL SYMPOSIUM LATTICE FIELD
THEORY, DALLAS, USA, OCTOBER 12--16, 1993 3 pages preprint HU
BERLIN--IEP--93/5 and BIELEFELD BI-TP--93/63, November 199
Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD
We calculate numerically universal finite-size-scaling functions of the
magnetization for the three-dimensional O(4) and O(2) spin models. The approach
of these functions to the infinite-volume scaling functions is studied in
detail on the critical and pseudocritical lines. For this purpose we determine
the pseudocritical line in two different ways. We find that the asymptotic form
of the finite-size-scaling functions is already reached at small values of the
scaling variable. A comparison with QCD lattice data for two flavours of
staggered fermions shows a similar finite-size behaviour which is compatible
with that of the spin models.Comment: Lattice2001(hightemp), 3 pages, 5 figures, acknowledgements
completed, minor typographical errors correcte
External field dependence of the correlation lengths in the three-dimensional O(4) model
We investigate numerically the transverse and longitudinal correlation
lengths of the three-dimensional O(4) model as a function of the external field
H. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of
the transverse correlation length, which is expected due to the Goldstone modes
of the model. On the critical line we find the universal amplitude ratio xi^c_T
/ xi^c_L = 1.99(1). From our data we derive the universal scaling function for
the transverse correlation length. The H-dependencies of the correlation
lengths in the high temperature phase are discussed and shown to be in accord
with the scaling functions.Comment: 3 pages, 4 figures, Lattice2003(higgs) contribution, espcrc2.st
Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge Theory
We calculate the critical amplitudes of the Polyakov loop and its
susceptibility at the deconfinement transition of SU(2) gauge theory. To this
end we carefully study the corrections to the scaling functions of the
observables coming from irrelevant exponents. As a guiding line for determining
the critical amplitudes we use envelope equations derived from the finite size
scaling formulae for the observables. The equations are then evaluated with new
high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find
different correction-to-scaling behaviours above and below the transition. Our
result for the universal ratio of the susceptibility amplitudes is
C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d
Ising model.Comment: LATTICE98(hightemp
The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects
We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on to lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
We find, that for lattices of size and larger the crossover peak is
independent of lattice size at and has a peak height of
. We conclude therefore that the crossover peak is not the
result of an ordinary phase transition. Further, the contributions to
from different plaquette correlations are calculated. We find, that at the peak
and far outside the peak the ratio of contributions from orthogonal and
parallel plaquette correlations is different. To estimate the finite
temperature influence on symmetric lattices far off the deconfinement
transition point we calculate the modulus of the lattice average of the
Polyakov loop on these lattices and compare it to predictions from a random
walk model.Comment: Latex 2e,10 pages including 5 postscript figure
Finite size analysis of the pseudo specific heat in SU(2) gauge theory
We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on to lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
In this context we calculate the modulus of the lattice average of the Polyakov
loop on symmetric lattices and compare it to the prediction from a random walk
model.Comment: Talk presented at LATTICE96(finite temperature), 3 pages, 4
Postscript figure
Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the -method
We determine the critical point and the ratios and
of critical exponents of the deconfinement transition in gauge theory
by applying the -method to Monte Carlo data of the modulus and the
square of the Polyakov loop. With the same technique we find from the Binder
cumulant its universal value at the critical point in the thermodynamical
limit to and for the next-to-leading exponent .
From the derivatives of the Polyakov loop dependent quantities we estimate then
. The result from the derivative of is , in
complete agreement with that of the Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te
Non-perturbative determination of anisotropy coefficients in lattice gauge theories
We propose a new non-perturbative method to compute derivatives of gauge
coupling constants with respect to anisotropic lattice spacings (anisotropy
coefficients), which are required in an evaluation of thermodynamic quantities
from numerical simulations on the lattice. Our method is based on a precise
measurement of the finite temperature deconfining transition curve in the
lattice coupling parameter space extended to anisotropic lattices by applying
the spectral density method. We test the method for the cases of SU(2) and
SU(3) gauge theories at the deconfining transition point on lattices with the
lattice size in the time direction -- 6. In both cases, there is a
clear discrepancy between our results and perturbative values. A longstanding
problem, when one uses the perturbative anisotropy coefficients, is a
non-vanishing pressure gap at the deconfining transition point in the SU(3)
gauge theory. Using our non-perturbative anisotropy coefficients, we find that
this problem is completely resolved: we obtain and
on and 6 lattices, respectively.Comment: 24pages,7figures,5table
Numerical equation of state and other scaling functions from an improved three-dimensional Ising model
We study an improved three-dimensional Ising model with external magnetic
field near the critical point by Monte Carlo simulations. From our data we
determine numerically the universal scaling functions of the magnetization,
that is the equation of state, of the susceptibility and of the correlation
length. In order to normalize the scaling functions we calculate the critical
amplitudes of the three observables on the critical line, the phase boundary
and the critical isochore. These amplitudes lead to the universal ratios
C^+/C^-=4.756(28), R_{chi}=1.723(13), Q_c=0.326(3) and Q_2=1.201(10). We find
excellent agreement of the data with the parametric representation of the
asymptotic equation of state as found by field theory methods. The comparison
of the susceptibility data to the corresponding scaling function shows a
marginal difference in the symmetric phase, which can be explained by the
slightly different value for R_{chi} used in the parametrization. The shape of
the correlation-length-scaling function is similar to the one of the
susceptibility, as expected from earlier parametrizations. The peak positions
of the two scaling functions are coinciding within the error bars.Comment: 27 pages, 14 Ps-figures, Latex2e, 10 pages added, including the
scaling function of the correlation length, to appear in Nucl. Phys.
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