3,172 research outputs found
Finite density QCD with heavy quarks
In the large fermion mass limit of QCD at finite density the structure of the
partition function greatly simplifies and can be studied analytically. We show
that, contrary to general wisdom, the phase of the Dirac determinant is
relevant only at finite temperature and can be neglected for zero temperature
fields.Comment: LATTICE98(hightemp), 3 pages, 3 figure
Frustration in Finite Density QCD
We present a detailed analysis of the QCD partition function in the Grand
Canonical formalism. Using the fugacity expansion we find evidence for
numerical instabilities in the standard evaluation of its coefficients. We
discuss the origin of this problem and propose an issue to it. The correct
analysis shows no evidence for a discontinuity in the baryonic density in the
strong coupling limit. The moderate optimism that was inspired by the Grand
Canonical Partition Function calculations in the last years has to be
considered ill-founded.Comment: 9 pages, 6 Postscript figures; some comments adde
Phase transition(s) in finite density QCD
The Grand Canonical formalism is generally used in numerical simulations of
finite density QCD since it allows free mobility in the chemical potential
. We show that special care has to be used in extracting numerical results
to avoid dramatic rounding effects and spurious transition signals. If we
analyze data correctly, with reasonable statistics, no signal of first order
phase transition is present and results using the Glasgow prescription are
practically coincident with the ones obtained using the modulus of the
fermionic determinant.Comment: 6 pages, 5 ps figs. To appear in Proceedings of "QCD at Finite Baryon
Density" workshop, Bielefeld, 27-30 April 199
Three and Two Colours Finite Density QCD at Strong Coupling: A New Look
Simulations in finite density, beta=0 lattice QCD by means of the
Monomer-Dimer-Polymer algorithm show a signal of first order transition at
finite temporal size. This behaviour agrees with predictions of the mean field
approximation, but is difficult to reconcile with infinite mass analytical
solution. The MDP simulations are considered in detail and severe convergence
problems are found for the SU(3) gauge group, in a wide region of chemical
potential. Simulations of SU(2) model show discrepancies with MDP results as
well.Comment: 18 pages, 9 figures, to appear in Nucl. Phys.
Finite Density Fat QCD
Lattice formulation of Finite Baryon Density QCD is problematic from computer
simulation point of view; it is well known that for light quark masses the
reconstructed partition function fails to be positive in a wide region of
parameter space. For large bare quark masses, instead, it is possible to obtain
more sensible results; problems are still present but restricted to a small
region. We present evidence for a saturation transition independent from the
gauge coupling and for a transition line that, starting from the
temperature critical point at , moves towards smaller with
increasing as expected from simplified phenomenological arguments.Comment: 14 pages, 10 figure
Rigorous arguments against current wisdoms in finite density QCD
QCD at finite chemical potential is analytically investigated in the region
of large bare fermion masses. We show that, contrary to the general wisdom, the
phase of the fermion determinant is irrelevant at zero temperature. However if
the system is put at finite temperature, the contribution of the phase is
finite. We also discuss on the quenched approximation and suggest that the
origin of the failure of this approximation in finite density QCD could relay
on the fundamental role that Pauli exclusion principle plays in this case.Comment: 16 pages, 5 figure
New Ideas in Finite Density QCD
We introduce a new approach to analyze the phase diagram of QCD at finite
chemical potential and temperature, based on the definition of a generalized
QCD action. Several details of the method will be discussed, with particular
emphasis on the advantages respect to the imaginary chemical potential
approach.Comment: Talk presented at Lattice2004 (non-zero), Fermilab, June 21-26, 2004;
3 pages, 2 figure
On Stein's method and perturbations
Steinâs (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Steinâs method, one needs to establish a Stein identity for the approximating distribution, solve the Stein equation and estimate the behaviour of the solutions in terms of the metrics under study. For some Stein equations, solutions with good properties are known; for others, this is not the case.
Barbour and Xia (1999) introduced a perturbation method for Poisson approximation, in which Stein identities for a large class of compound Poisson and translated Poisson distributions are viewed as perturbations of a Poisson distribution. In this paper, it is shown that the method can be extended to very general settings, including perturbations of normal, Poisson, compound Poisson, binomial and Poisson process approximations in terms of various metrics such as the Kolmogorov, Wasserstein and total variation metrics. Examples are provided to illustrate how the general perturbation method can be applied
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