4,750 research outputs found
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
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
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
A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model
We investigate numerically the three-dimensional O(2) model on 8^3-160^3
lattices as a function of the magnetic field H. In the low-temperature phase we
verify the H-dependence of the magnetization M induced by the Goldstone modes
and determine M in the thermodynamic limit on the coexistence line both by
extrapolation and by chiral perturbation theory. We compute two critical
amplitudes from the scaling behaviours on the coexistence line and on the
critical line. In both cases we find negative corrections to scaling. With
additional high temperature data we calculate the scaling function and show
that it has a smaller slope than that of the O(4) model. For future tests of
QCD lattice data we study as well finite-size-scaling functions.Comment: Lattice 2000 (Spin Models), minor typographic errors fixe
Specific heat and energy for the three-dimensional O(2) model
We investigate the three-dimensional O(2) model on lattices of size 8^3 to
160^3 close to the critical point at zero magnetic field. We confirm explicitly
the value of the critical coupling J_c found by Ballesteros et al. and estimate
there the universal values of g_r and xi/L. At the critical point we study the
finite size dependencies of the energy density epsilon and the specific heat C.
We find that the nonsingular part of the specific heat C_{ns} is linearly
dependent on 1/alpha. From the critical behaviour of the specific heat for T
not T_c on the largest lattices we determine the universal amplitude ratio
A+/A-. The alpha- dependence of this ratio is close to the phenomenological
relation A+/A- = 1-4alpha.Comment: Lattice2001(spin), 3 pages, 4 figure
The chiral transition of N_f=2 QCD with fundamental and adjoint fermions
We study QCD with two staggered Dirac fermions both in the fundamental (QCD)
and the adjoint representation (aQCD) near the chiral transition. The aim is to
find the universality class of the chiral transition and to verify Goldstone
effects below the transition. We investigate aQCD, because in that theory the
deconfinement and the chiral transitions occur at different temperatures
T_d<T_c. Here, we show that the scaling behaviour of the chiral condensate in
the vicinity of \beta_c is in full agreeement with that of the 3d O(2)
universality class. In the region T_d<T<T_c we confirm the quark mass
dependence of the chiral condensate which is expected due to the existence of
Goldstone modes like in 3d O(N) spin models. For fundamental QCD we use the
p4-action. Here, we find Goldstone effects below T_c like in aQCD and the 3d
O(N) spin models, however no O(2)/O(4) scaling near the chiral transition
point. The result for QCD may be a consequence of the coincidence of the
deconfinement transition with the chiral transition.Comment: 6 pages, 5 figures, poster contribution to Lattice 2005 (Nonzero
temperature and density), one reference added, figure 2 change
Polyakov loop and spin correlators on finite lattices A study beyond the mass gap
We derive an analytic expression for point-to-point correlation functions of
the Polyakov loop based on the transfer matrix formalism. For the Ising
model we show that the results deduced from point-point spin correlators are
coinciding with those from zero momentum correlators. We investigate the
contributions from eigenvalues of the transfer matrix beyond the mass gap and
discuss the limitations and possibilities of such an analysis. The finite size
behaviour of the obtained Ising model matrix elements is examined. The
point-to-point correlator formula is then applied to Polyakov loop data in
finite temperature gauge theory. The leading matrix element shows all
expected scaling properties. Just above the critical point we find a Debye
screening mass , independent of the volume.Comment: 13 pages and 8 figures, late
- âŠ