68 research outputs found
QCD critical point and event-by-event fluctuations in heavy ion collisions
A summary of work done in collaboration with K. Rajagopal and E. Shuryak. We
show how heavy ion collision experiments, in particular, event-by-event
fluctuation measurements, can lead to the discovery of the critical point on
the phase diagram of QCD.Comment: 4 pages. Summary of work done in collaboration with K. Rajagopal and
E. Shuryak (hep-ph/9903292). To be published in the proceedings of Quark
Matter 99, Torino, Italy, May 10-14, 199
Universal correlations in spectra of the lattice QCD Dirac operator
Recently, Kalkreuter obtained complete Dirac spectra for lattice
gauge theory both for staggered fermions and for Wilson fermions. The lattice
size was as large as . We performed a statistical analysis of these data
and found that the eigenvalue correlations can be described by the Gaussian
Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal
Ensemble for Wilson fermions. In both cases long range spectral fluctuations
are strongly suppressed: the variance of a sequence of levels containing
eigenvalues on average is given by
( is equal to 4 and 1, respectively) instead of for a
random sequence of levels. Our findings are in agreement with the anti-unitary
symmetry of the lattice Dirac operator for with staggered fermions
which differs from Wilson fermions (with the continuum anti-unitary symmetry).
For , we predict that the eigenvalue correlations are given by the
Gaussian Unitary Ensemble.Comment: Talk present at LATTICE96(chirality in QCD), 3 pages, Late
Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
Monte Carlo simulations of finite density systems are often plagued by the
complex action problem. We point out that there exists certain
non-commutativity in the zero chemical potential limit and the thermodynamic
limit when one tries to study such systems by reweighting techniques. This is
demonstrated by explicit calculations in a Random Matrix Theory, which is
thought to be a simple qualitative model for finite density QCD. The
factorization method allows us to understand how the non-commutativity, which
appears at the intermediate steps, cancels in the end results for physical
observables.Comment: 7 pages, 9 figure
Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps
file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised
version, to appear in PRD, minor modifications and corrected typos, Fig.4
revise
Critical point of QCD at finite T and \mu, lattice results for physical quark masses
A critical point (E) is expected in QCD on the temperature (T) versus
baryonic chemical potential (\mu) plane. Using a recently proposed lattice
method for \mu \neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of
physical masses on L_t=4 lattices. Our result for the critical point is T_E=162
\pm 2 MeV and \mu_E= 360 \pm 40 MeV. For the critical temperature at \mu=0 we
obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and
S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark
masses (m_{u,d}) by a factor of three down to their physical values.
Furthermore, in order to approach the thermodynamical limit we increase our
largest volume by a factor of three. As expected, decreasing m_{u,d} decreased
\mu_E. Note, that the continuum extrapolation is still missingComment: 10 pages, 2 figure
The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory
We introduce a random matrix model with the symmetries of QCD at finite
temperature and chemical potentials for baryon number and isospin. We analyze
the phase diagram of this model in the chemical potential plane for different
temperatures and quark masses. We find a rich phase structure with five
different phases separated by both first and second order lines. The phases are
characterized by the pion condensate and the chiral condensate for each of the
flavors. In agreement with lattice simulations, we find that in the phase with
zero pion condensate the critical temperature depends in the same way on the
baryon number chemical potential and on the isospin chemical potential. At
nonzero quark mass, we remarkably find that the critical end point at nonzero
temperature and baryon chemical potential is split in two by an arbitrarily
small isospin chemical potential. As a consequence, there are two crossovers
that separate the hadronic phase from the quark-gluon plasma phase at high
temperature. Detailed analytical results are obtained at zero temperature and
in the chiral limit.Comment: 13 pages, 5 figures, REVTeX
Impossibility of spontaneously breaking local symmetries and the sign problem
Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.Comment: Latex 6 page
Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state
Lack of Lorentz invariance of QCD at finite quark chemical potential in
general implies the need of Lorentz non-invariant condensates for the
self-consistent description of the color-superconducting ground state.
Moreover, the spontaneous breakdown of color SU(3) in this state naturally
leads to the existence of SU(3) non-invariant non-superconducting expectation
values. We illustrate these observations by analyzing the properties of an
effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the
possibility of color-superconducting states with effectively gapless fermionic
excitations. It turns out that the effect of condensates so far neglected can
yield new interesting phenomena.Comment: 16 pages, 3 figure
Lattice determination of the critical point of QCD at finite T and \mu
Based on universal arguments it is believed that there is a critical point
(E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which
is of extreme importance for heavy-ion experiments. Using finite size scaling
and a recently proposed lattice method to study QCD at finite \mu we determine
the location of E in QCD with n_f=2+1 dynamical staggered quarks with
semi-realistic masses on lattices. Our result is T_E=160 \pm 3.5 MeV
and \mu_E= 725 \pm 35 MeV. For the critical temperature at \mu=0 we obtained
T_c=172 \pm 3 MeV.Comment: misprints corrected, version to appear in JHE
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