6,196 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 $2d$ Ising model and in finite temperature
$SU(2)$ gauge theory. We find that the leading matrix element shows similar
scaling properties in both models. Just above the critical point we obtain for
$SU(2)$ a Debye screening mass $~\mu_D/T\approx4~$, 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

### 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 $4^4$ to $16^4$ 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 $8^4$ and larger the crossover peak is
independent of lattice size at $\beta_{co}=2.23(2)$ and has a peak height of
$C_{V,co}=1.685(10)$. We conclude therefore that the crossover peak is not the
result of an ordinary phase transition. Further, the contributions to $C_V$
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 $4^4$ to $16^4$ 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 $\chi^2$-method

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$
of critical exponents of the deconfinement transition in $SU(2)$ gauge theory
by applying the $\chi^2$-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 $g_r$ its universal value at the critical point in the thermodynamical
limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$.
From the derivatives of the Polyakov loop dependent quantities we estimate then
$1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in
complete agreement with that of the $3d$ 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 $N_t=4$ -- 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 $\Delta p/T^4 = 0.001(15)$ and
$-0.003(17)$ on $N_t=4$ and 6 lattices, respectively.Comment: 24pages,7figures,5table

### Longitudinal and transverse spectral functions in the three-dimensional O(4) model

We have performed a high statistics simulation of the O(4) model on a
three-dimensional lattice of linear extension L=120 for small external fields
H. Using the maximum entropy method we analyze the longitudinal and transverse
plane spin correlation functions for T=T_c. In the transverse case
we find for all T and H a single sharp peak in the spectral function, whose
position defines the transverse mass m_T, the correlator is that of a free
particle with mass m_T. In the longitudinal case we find in the very high
temperature region also a single sharp peak in the spectrum. On approaching the
critical point from above the peak broadens somewhat and at T_c its position
m_L is at 2m_T for all our H-values. Below T_c we find still a significant peak
at omega=2m_T and at higher omega-values a continuum of states with several
smaller peaks with decreasing heights. This finding is in accord with a
relation of Patashinskii and Pokrovskii between the longitudinal and the
transverse correlation functions. We test this relation in the following. As a
by-product we calculate critical exponents and amplitudes and confirm our
former results.Comment: 38 pages, 26 figure

### 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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