3,451 research outputs found
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
Critical behavior of 3D SU(2) gauge theory at finite temperature: exact results from universality
We show that universality arguments, namely the Svetitsky-Yaffe conjecture,
allow one to obtain exact results on the critical behavior of 3D SU(2) gauge
theory at the finite temperature deconfinement transition,through a mapping
into the 2D Ising model. In particular, we consider the finite-size scaling
behavior of the plaquette operator, which can be mapped into the energy
operator of the 2D Ising model. We obtain exact predictions for the dependence
of the plaquette expectation value on the size and shape of the lattice and we
compare them to Monte Carlo results, finding complete agreement. We discuss the
application of this method to the computation of more general correlators of
the plaquette operator at criticality, and its relevance to the study of the
color flux tube structure.Comment: 10 pages, LaTeX file + 3 eps figure
Scaling Properties of the Energy Density in SU(2) Lattice Gauge Theory
The lattice data for the energy density of gauge theory are
calculated with \nop~derivatives of the coupling constants. These derivatives
are obtained from two sources : i) a parametrization of the \nop~beta function
in accord with the measured critical temperature and values and
ii) a \nop~calculation of the presssure. We then perform a detailed finite size
scaling analysis of the energy density near . It is shown that at the
critical temperature the energy density is scaling as a function of with
the corresponding Ising model critical exponents. The value of
in the continuum limit is estimated to be 0.256(23). In
the high temperature regime the energy density is approaching its weak coupling
limit from below, at it has reached only about of the
limit.Comment: 15 pages + 9 figures, BI-TP 94/3
Critical behaviour and scaling functions of the three-dimensional O(6) model
We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3
lattices within the critical region at zero magnetic field, as well as at
finite magnetic field on the critical isotherm and for several fixed couplings
in the broken and the symmetric phase. We obtain from the Binder cumulant at
vanishing magnetic field the critical coupling J_c=1.42865(3). The universal
value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the
critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and
\nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore,
we verify predicted effects induced by massless Goldstone modes in the broken
phase. The results are well described by the perturbative form of the model's
equation of state. Our O(6)-result is compared to the corresponding Ising, O(2)
and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour
of the magnetisation on the pseudocritical line.Comment: 13 pages, 20 figures, REVTEX, fixed an error in the determination of
R_\chi and changed the corresponding line in figure 13
The Thermodynamics of Quarks and Gluons
This is an introduction to the study of strongly interacting matter. We
survey its different possible states and discuss the transition from hadronic
matter to a plasma of deconfined quarks and gluons. Following this, we
summarize the results provided by lattice QCD finite temperature and density,
and then investigate the nature of the deconfinement transition. Finally we
give a schematic overview of possible ways to study the properties of the
quark-gluon plasma.Comment: 19 pages, 21 figures; lecture given at the QGP Winter School,
Jaipur/India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic
The beta function and equation of state for QCD with two flavors of quarks
We measure the pressure and energy density of two flavor QCD in a wide range
of quark masses and temperatures. The pressure is obtained from an integral
over the average plaquette or psi-bar-psi. We measure the QCD beta function,
including the anomalous dimension of the quark mass, in new Monte Carlo
simulations and from results in the literature. We use it to find the
interaction measure, E-3p, yielding non-perturbative values for both the energy
density E and the pressure p. uuencoded compressed PostScript file Revised
version should work on more PostScript printers.Comment: 24 page
Rapidly rotating Bose-Einstein condensates in anharmonic potentials
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can
exhibit a rich variety of vortex phases, including a vortex lattice, a vortex
lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi
variational approach to determine the ground state of the condensate in the
rotating frame -- valid for sufficiently strongly interacting condensates -- we
determine the transitions between these three phases for a
quadratic-plus-quartic confining potential. Combining the present results with
previous numerical simulations of small rotating condensates in such anharmonic
potentials, we delineate the general structure of the zero temperature phase
diagram.Comment: 5 pages, 5 figure
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