697 research outputs found
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
Color Superconductivity in Asymmetric Matter
The influence of different chemical potential for different flavors on color
superconductivity is analyzed.
It is found that there is a first order transition as the asymmetry grows.
This transition proceeds through the formation of bubbles of low density,
flavor asymmetric normal phase inside a high density, superconducting phase
with a gap {\it larger} than the one found in the symmetric case. For small
fixed asymmetries the system is normal at low densities and superconducting
only above some critical density. For larger asymmetries the two massless
quarks system stays in the mixed state for arbitrarily high densities.Comment: 8 pages, 2 figure
Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
In quantum chromodynamics (QCD) at nonzero chemical potential, the
eigenvalues of the Dirac operator are scattered in the complex plane. Can the
fluctuation properties of the Dirac spectrum be described by universal
predictions of non-Hermitian random matrix theory? We introduce an unfolding
procedure for complex eigenvalues and apply it to data from lattice QCD at
finite chemical potential to construct the nearest-neighbor spacing
distribution of adjacent eigenvalues in the complex plane. For intermediate
values of , we find agreement with predictions of the Ginibre ensemble of
random matrix theory, both in the confinement and in the deconfinement phase.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
Imaginary chemical potential and finite fermion density on the lattice
Standard lattice fermion algorithms run into the well-known sign problem at
real chemical potential. In this paper we investigate the possibility of using
imaginary chemical potential, and argue that it has advantages over other
methods, particularly for probing the physics at finite temperature as well as
density. As a feasibility study, we present numerical results for the partition
function of the two-dimensional Hubbard model with imaginary chemical
potential.
We also note that systems with a net imbalance of isospin may be simulated
using a real chemical potential that couples to I_3 without suffering from the
sign problem.Comment: 9 pages, LaTe
The Fractal Geometry of Critical Systems
We investigate the geometry of a critical system undergoing a second order
thermal phase transition. Using a local description for the dynamics
characterizing the system at the critical point T=Tc, we reveal the formation
of clusters with fractal geometry, where the term cluster is used to describe
regions with a nonvanishing value of the order parameter. We show that,
treating the cluster as an open subsystem of the entire system, new
instanton-like configurations dominate the statistical mechanics of the
cluster. We study the dependence of the resulting fractal dimension on the
embedding dimension and the scaling properties (isothermal critical exponent)
of the system. Taking into account the finite size effects we are able to
calculate the size of the critical cluster in terms of the total size of the
system, the critical temperature and the effective coupling of the long
wavelength interaction at the critical point. We also show that the size of the
cluster has to be identified with the correlation length at criticality.
Finally, within the framework of the mean field approximation, we extend our
local considerations to obtain a global description of the system.Comment: 1 LaTeX file, 4 figures in ps-files. Accepted for publication in
Physical Review
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
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
Quantum Chaos in the Yang-Mills-Higgs System at Finite Temperature
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is
studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs
is calculated within thermofield dynamics. Level statistics of the spectra is
studied by plotting nearest-level spacing distribution histograms. It is found
that finite temperature effects lead to a strengthening of chaotic effects,
i.e. spectrum which has Poissonian distribution at zero temperature has
Gaussian distribution at finite-temperature.Comment: 6 pages, 5 figures, Revte
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
Fermion determinants in matrix models of QCD at nonzero chemical potential
The presence of a chemical potential completely changes the analytical
structure of the QCD partition function. In particular, the eigenvalues of the
Dirac operator are distributed over a finite area in the complex plane, whereas
the zeros of the partition function in the complex mass plane remain on a
curve. In this paper we study the effects of the fermion determinant at nonzero
chemical potential on the Dirac spectrum by means of the resolvent, G(z), of
the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1)
model (Gibbs model) and in a random matrix model with the global symmetries of
the QCD partition function. In both cases we find that, if the argument z of
the resolvent is not equal to the mass m in the fermion determinant, the
resolvent diverges in the thermodynamic limit. However, for z =m the resolvent
in both models is well defined. In particular, the nature of the limit is illuminated in the Gibbs model. The phase structure of the
random matrix model in the complex m and \mu-planes is investigated both by a
saddle point approximation and via the distribution of Yang-Lee zeros. Both
methods are in complete agreement and lead to a well-defined chiral condensate
and quark number density.Comment: 27 pages, 6 figures, Late
- …