521 research outputs found

### Towards a controlled study of the QCD critical point

The phase diagram of QCD, as a function of temperature T and quark chemical
potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative
nature makes it a natural object of lattice studies. However, the sign problem
prevents the application of standard Monte Carlo techniques at non-zero baryon
density. We have been pursuing an approach free of the sign problem, where the
chemical potential is taken as imaginary and the results are Taylor-expanded in
mu/T about mu=0, then analytically continued to real mu.
Within this approach we have determined the sensitivity of the critical
chemical potential mu_E to the quark mass, d(\mu_E)^2/dm_q|_{\mu_E=0}. Our
study indicates that the critical point moves to {\em smaller} chemical
potential as the quark mass {\em increases}. This finding, contrary to common
wisdom, implies that the deconfinement crossover, which takes place in QCD at
mu=0 when the temperature is raised, will remain a crossover in the mu-region
where our Taylor expansion can be trusted. If this result, obtained on a coarse
lattice, is confirmed by simulations on finer lattices now in progress, then we
predict that no {\em chiral} critical point will be found for mu_B \lesssim 500
MeV, unless the phase diagram contains additional transitions.Comment: 4 pages, 6 figures, proceedings of Quark Matter 2008, Jaipur (India),
Feb. 2008, to appear in J. Phys.

### QCD phase diagram for small densities from simulations at imaginary mu

We present results on the QCD phase diagram for small densities without
reweighting. Our simulations are performed with an imaginary chemical potential
mu_I for which the fermion determinant is positive. On an 8^3x4 lattice with 2
flavors of staggered quarks, we map out the pseudo-critical temperature
T_c(mu_I). For mu_I/T < pi/3, this is an analytic function whose Taylor
expansion converges rapidly, with truncation errors smaller than statistical
ones. The result is analytically continued to give the location of the
pseudo-critical line for real mu_B<500 MeV.Comment: Lattice2002(nonzerot), 3 pp, 5 figure

### Evading the sign problem in random matrix simulations

We show how the sign problem occurring in dynamical simulations of random
matrices at nonzero chemical potential can be avoided by judiciously combining
matrices into subsets. For each subset the sum of fermionic determinants is
real and positive such that importance sampling can be used in Monte Carlo
simulations. The number of matrices per subset is proportional to the matrix
dimension. We measure the chiral condensate and observe that the statistical
error is independent of the chemical potential and grows linearly with the
matrix dimension, which contrasts strongly with its exponential growth in
reweighting methods.Comment: 4 pages, 3 figures, minor corrections, as published in Phys. Rev.
Let

### Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

We study the strange quark mass dependence of the tricritical point of the
U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the
tricritical point is at a large strange mass value, the strange sector as well
as the \eta-a_0 sector decouples from the light degrees of freedom which
determines the thermodynamics. By tracing this decoupling we arrive from the
original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R
symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta
functions for the running of the parameters in each of these models and
tree-level matching of the coupling of these models performed at intermediate
scales are used to determine the influence of the heavy sector on the
parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the
thermodynamics of this latter model we identified the tricritical surface of
the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the
results for QCD we used different scenarios for the m_s and \mu_q dependence of
the effective model parameters, then the \mu_q^TCP(m_s) function can be
determined. Depending on the details, a curve bending upwards or downwards near
\mu_q=0 can be obtained, while with explicit chemical potential dependence of
the parameters the direction of the curve can change with m_s, too.Comment: 17 pages, 6 figures, uses revtex4-

### Lattice baryons in the 1/N expansion

Results are presented for hadron spectroscopy with gauge groups SU(N) with
N=3, 5, 7. Calculations use the quenched approximation. Lattice spacings are
matched using the static potential. Meson spectra show independence on N and
vacuum-to-hadron matrix elements scale as the square root of N. The baryon
spectrum shows the excitation levels of a rigid rotor.Comment: 19 pages, 11 figure

### Model analysis of thermal UV-cutoff effects on the chiral critical surface at finite temperature and chemical potential

We study the effects of temporal UV-cutoff on the chiral critical surface in
hot and dense QCD using a chiral effective model. Recent lattice QCD
simulations indicate that the curvature of the critical surface might change
toward the direction in which the first order phase transition becomes stronger
on increasing the number of lattice sites. To investigate this effect on the
critical surface in an effective model approach, we use the Nambu-Jona-Lasinio
model with finite Matsubara frequency summation. We find that qualitative
feature of the critical surface does not alter appreciably as we decrease the
summation number, which is unlike the case what is observed in the recent
lattice QCD studies. This may either suggest the dependence of chemical
potential on the coupling strength or due to some additional interacting terms
such as vector interactions which could play an important role at finite
density.Comment: 7 pages, 8 figure

### Degrees of freedom and the phase transitions of two flavor QCD

We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the
linear sigma model extended by including a Polyakov loop potential, which is
fitted to reproduce pure gauge theory thermodynamics, and a coupling between
the chiral fields and the Polyakov loop. Thus the resulting models have as
relevant degrees of freedom the Polyakov loop and chiral fields. By comparing
the extended models with the bare chiral models we can conclude that the
addition of the Polyakov loop is necessary in order to obtain both
qualitatively and quantitatively correct results at finite temperatures. These
results are extended to finite net quark densities, several thermodynamical
quantites are investigated in detail and possible applications and consequences
for relativistic heavy ion collision phenomenology are discussed

### Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence from lattice simulations of QCD with three
degenerate quark species for two tricritical points in the (T,m) phase diagram
at fixed imaginary \mu/T=i\pi/3 mod 2\pi/3, one in the light and one in the
heavy mass regime. These represent the boundaries of the chiral and
deconfinement critical lines continued to imaginary chemical potential,
respectively. It is demonstrated that the shape of the deconfinement critical
line for real chemical potentials is dictated by tricritical scaling and
implies the weakening of the deconfinement transition with real chemical
potential. The generalization to non-degenerate and light quark masses is
discussed.Comment: 4 pages, 5 figure

### A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix
simulations of a two-matrix model at nonzero chemical potential. The sign
problem, caused by the complex fermion determinants, is solved by gathering the
matrices into subsets, whose sums of determinants are real and positive even
though their cardinality only grows linearly with the matrix size. A detailed
proof of this positivity theorem is given for an arbitrary number of fermion
flavors. We performed importance sampling Monte Carlo simulations to compute
the chiral condensate and the quark number density for varying chemical
potential and volume. The statistical errors on the results only show a mild
dependence on the matrix size and chemical potential, which confirms the
absence of sign problem in the subset method. This strongly contrasts with the
exponential growth of the statistical error in standard reweighting methods,
which was also analyzed quantitatively using the subset method. Finally, we
show how the method elegantly resolves the Silver Blaze puzzle in the
microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references;
in Sec. VB: added discussion of model satisfying the Silver Blaze for all N
(proof in Appendix E

### Finite isospin density probe for conformality

A new method of employing an isospin chemical potential for QCD-like theories
with different number of colors, number of fermion flavors, and in different
fermion representations is proposed. The isospin chemical potential, which can
be simulated on the lattice due to its positive definite determinant gives a
means to probe both confining theories and IR conformal theories without
adjusting the lattice spacing and size. As the quark mass is reduced, the
isospin chemical potential provides an avenue to extract the chiral condensate
in confining theories through the resulting pseudoscalar condensate. For IR
conformal theories, the mass anomalous dimension can be extracted in the
conformal window through "finite density" scaling since the isospin chemical
potential is coupled to a conserved current. In both of these approaches, the
isospin chemical potential can be continuously varied for each ensemble at
comparable costs while maintaining the hierarchy between the lattice size and
lattice spacing. In addition to exploring these methods, finite volume and
lattice spacing effects are investigated.Comment: 18 pages, 3 figures, v3: typos corrected and discussions improved.
Phys. Rev. D 85, 074503 (2012

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