38 research outputs found
Pressure and non-linear susceptibilities in QCD at finite chemical potentials
When the free energy density of QCD is expanded in a series in the chemical
potential, mu, the Taylor coefficients are the non-linear quark number
susceptibilities. We show that these depend on the prescription for putting
chemical potential on the lattice, making all extrapolations in chemical
potential prescription dependent at finite lattice spacing. To put bounds on
the prescription dependence, we investigate the magnitude of the non-linear
susceptibilities over a range of temperature, T, in QCD with two degenerate
flavours of light dynamical quarks at lattice spacing 1/4T. The prescription
dependence is removed in quenched QCD through a continuum extrapolation, and
the dependence of the pressure, P, on mu is obtained.Comment: 15 pages, 2 figures. Data on chi_uuuu added, discussion enhance
The QCD thermal phase transition in the presence of a small chemical potential
We propose a new method to investigate the thermal properties of QCD with a
small quark chemical potential . Derivatives of the phase transition point
with respect to are computed at for 2 flavors of p-4 improved
staggered fermions with on a lattice. The resulting
Taylor expansion is well behaved for the small values of relevant for RHIC phenomenology, and predicts a critical curve
in reasonable agreement with estimates obtained using exact
reweighting. In addition, we contrast the case of isoscalar and isovector
chemical potentials, quantify the effect of on the equation of
state, and comment on the complex phase of the fermion determinant in QCD with
.Comment: 26 pages, 25 figures, minor modificatio
Remarks on the multi-parameter reweighting method for the study of lattice QCD at non-zero temperature and density
We comment on the reweighting method for the study of finite density lattice
QCD. We discuss the applicable parameter range of the reweighting method for
models which have more than one simulation parameter. The applicability range
is determined by the fluctuations of the modification factor of the Boltzmann
weight. In some models having a first order phase transition, the fluctuations
are minimized along the phase transition line if we assume that the pressure in
the hot and the cold phase is balanced at the first order phase transition
point. This suggests that the reweighting method with two parameters is
applicable in a wide range for the purpose of tracing out the phase transition
line in the parameter space. To confirm the usefulness of the reweighting
method for 2 flavor QCD, the fluctuations of the reweighting factor are
measured by numerical simulations for the cases of reweighting in the quark
mass and chemical potential directions. The relation with the phase transition
line is discussed. Moreover, the sign problem caused by the complex phase
fluctuations is studied.Comment: 20 page, 6 figure
The Equation of State for Two Flavor QCD at Non-zero Chemical Potential
We present results of a simulation of QCD on a 4x16^3 lattice with 2
continuum flavors of p4-improved staggered fermion with mass m/T=0.4.
Derivatives of the thermodynamic grand potential with respect to quark chemical
potential mu_q up to fourth order are calculated, enabling estimates of the
pressure, quark number density and associated susceptibilities as functions of
mu_q via Taylor series expansion. Discretisation effects associated with
various staggered fermion formulations are discussed in some detail. In
addition it is possible to estimate the radius of convergence of the expansion
as a function of temperature. We also discuss the calculation of energy and
entropy densities which are defined via mixed derivatives of the thermodynamic
grand potential with respect to the bare couplings and quark masses.Comment: 30 pages, LaTeX2e File, 17 Postscript figure
Universality, the QCD critical/tricritical point and the quark number susceptibility
The quark number susceptibility near the QCD critical end-point (CEP), the
tricritical point (TCP) and the O(4) critical line at finite temperature and
quark chemical potential is investigated. Based on the universality argument
and numerical model calculations we propose a possibility that the hidden
tricritical point strongly affects the critical phenomena around the critical
end-point. We made a semi-quantitative study of the quark number susceptibility
near CEP/TCP for several quark masses on the basis of the
Cornwall-Jackiw-Tomboulis (CJT) potential for QCD in the improved-ladder
approximation. The results show that the susceptibility is enhanced in a wide
region around CEP inside which the critical exponent gradually changes from
that of CEP to that of TCP, indicating a crossover of different universality
classes.Comment: 18 pages, 10 figure
Perturbative QCD at non-zero chemical potential: Comparison with the large-Nf limit and apparent convergence
The perturbative three-loop result for the thermodynamic potential of QCD at
finite temperature and chemical potential as obtained in the framework of
dimensional reduction is compared with the exact result in the limit of large
flavor number. The apparent convergence of the former as well as possibilities
for optimization are investigated. Corresponding optimized results for full QCD
are given for the case of two massless quark flavors.Comment: REVTEX4, 4 pages, 3 color figures. v2: fig. 3 now includes also
lattice data for two-flavor QCD at nonzero chemical potentia
Thermodynamics of Large-N_f QCD at Finite Chemical Potential
We extend the previously obtained results for the thermodynamic potential of
hot QCD in the limit of large number of fermions to non-vanishing chemical
potential. We give exact results for the thermal pressure in the entire range
of temperature and chemical potential for which the presence of a Landau pole
is negligible numerically. In addition we compute linear and non-linear quark
susceptibilities at zero chemical potential, and the entropy at small
temperatures. We compare with the available perturbative results and determine
their range of applicability. Our numerical accuracy is sufficiently high to
check and verify existing results, including the recent perturbative results by
Vuorinen on quark number susceptibilities and the older results by Freedman and
McLerran on the pressure at zero temperature and high chemical potential. We
also obtain a number of perturbative coefficients at sixth order in the
coupling that have not yet been calculated analytically. In the case of both
non-zero temperature and non-zero chemical potential, we investigate the range
of validity of a scaling behaviour noticed recently in lattice calculations by
Fodor, Katz, and Szabo at moderately large chemical potential and find that it
breaks down rather abruptly at , which points to a
presumably generic obstruction for extrapolating data from small to large
chemical potential. At sufficiently small temperatures , we find
dominating non-Fermi-liquid contributions to the interaction part of the
entropy, which exhibits strong nonlinearity in the temperature and an excess
over the free-theory value.Comment: 18 pages, 7 figures, JHEP style; v2: several updates, rewritten and
extended sect. 3.4 covering now "Entropy at small temperatures and
non-Fermi-liquid behaviour"; v3: additional remarks at the end of sect. 3.4;
v4: minor corrections and additions (version to appear in JHEP
A strongly first order electroweak phase transition from strong symmetry-breaking interactions
We argue that a strongly first order electroweak phase transition is natural
in the presence of strong symmetry-breaking interactions, such as technicolor.
We demonstrate this using an effective linear scalar theory of the
symmetry-breaking sector.Comment: LaTex, 15 pages, 3 figures in EPS format. Phys. Rev. D approved
Typographically Correct version, minor grammatical change
Different definitions of the chemical potential with identical partition function in QCD on a lattice
It is shown that starting from one and the same transfer matrix formulation
of QCD on a lattice, it is possible to obtain both the action of Hasenfratz and
Karsch as well as an action where the chemical potential is not coupled to the
temporal links.Comment: 4 page
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