115 research outputs found

### Finite density QCD with a canonical approach

We present a canonical method where the properties of QCD are directly
obtained as a function of the baryon density rho, rather than the chemical
potential mu. We apply this method to the determination of the phase diagram of
four-flavor QCD. For a pion mass m_pi \sim 350 MeV, the first-order transition
between the hadronic and the plasma phase gives rise to a co-existence region
in the T-rho plane, which we study in detail, including the associated
interface tension. We obtain accurate results for systems containing up to 30
baryons and quark chemical potentials mu up to 2 T. Our T-mu phase diagram
agrees with the literature when mu/T \lesssim 1. At larger chemical potential,
we observe a ``bending down'' of the phase boundary. We compare the free energy
in the confined and deconfined phase with predictions from a hadron resonance
gas and from a free massless quark gas respectively.Comment: 6 pages, 9 figures, proceedings of "Workshop on Computational Hadron
Physics", Cyprus, Sept. 200

### QCD at zero baryon density

While the grand canonical partition function Z_{GC}(mu) with chemical
potential mu explicitly breaks the Z_3 symmetry with the Dirac determinant, the
canonical partition function at fixed baryon number Z_C(B) is manifestly
Z_3-symmetric. We compare Z_{GC}(mu=0) and Z_C(B=0) formally and by numerical
simulations, in particular with respect to properties of the deconfinement
transition. Differences between the two ensembles, for physical observables
characterising the phase transition, vanish with increasing lattice size. We
show numerically that the free energy density is the same for both ensembles in
the thermodynamic limit.Comment: Lattice2003(nonzero), 3 pages, 5 figure

### QCD at Zero Baryon Density and the Polyakov Loop Paradox

We compare the grand canonical partition function at fixed chemical potential
mu with the canonical partition function at fixed baryon number B, formally and
by numerical simulations at mu=0 and B=0 with four flavours of staggered
quarks. We verify that the free energy densities are equal in the thermodynamic
limit, and show that they can be well described by the hadron resonance gas at
T T_c.
Small differences between the two ensembles, for thermodynamic observables
characterising the deconfinement phase transition, vanish with increasing
lattice size. These differences are solely caused by contributions of non-zero
baryon density sectors, which are exponentially suppressed with increasing
volume. The Polyakov loop shows a different behaviour: for all temperatures and
volumes, its expectation value is exactly zero in the canonical formulation,
whereas it is always non-zero in the commonly used grand-canonical formulation.
We clarify this paradoxical difference, and show that the non-vanishing
Polyakov loop expectation value is due to contributions of non-zero triality
states, which are not physical, because they give zero contribution to the
partition function.Comment: 21 pages, 7 figure

### The $\theta$-term, CP$^{N-1}$ Model and the Inversion Approach in the Imaginary $\theta$ Method

The weak coupling region of CP$^{N-1}$ lattice field theory with the
$\theta$-term is investigated. Both the usual real theta method and the
imaginary theta method are studied. The latter was first proposed by Bhanot and
David. Azcoiti et al. proposed an inversion approach based on the imaginary
theta method. The role of the inversion approach is investigated in this paper.
A wide range of values of $h=-{\rm Im} \theta$ is studied, where $\theta$
denotes the magnitude of the topological term. Step-like behavior in the
$x$-$h$ relation (where $x=Q/V$, $Q$ is the topological charge, and $V$ is the
two dimensional volume) is found in the weak coupling region. The physical
meaning of the position of the step-like behavior is discussed. The inversion
approach is applied to weak coupling regions.Comment: PTPTEX, 17 pages with 13 figures. Some sentences were
correcte

### QCD at small baryon number

We consider the difficulties of finite density QCD from the canonical
formalism. We present results for small baryon numbers, where the sign problem
can be controlled, in particular by supplementing the mu=0 sampling with
imaginary mu ensembles. We initiate the thermodynamic study of few-nucleon
systems, starting with the measurement of the free energy of a few baryons in
the confined and deconfined phase. We present a simple model for the phase
transition, whose results are in good agreement with the literature, but extend
to lower temperatures.Comment: Lattice2004(nonzero), 3 pages, 3 figures. 1 reference adde

### The 3-state Potts model as a heavy quark finite density laboratory

The 3-D Z(3) Potts model is a model for finite temperature QCD with heavy
quarks. The chemical potential in QCD becomes an external magnetic field in the
Potts model. Following Alford et al.\cite{Alford_et_al}, we revisit this
mapping, and determine the phase diagram for an arbitrary chemical potential,
real or imaginary. Analytic continuation of the phase transition line between
real and imaginary chemical potential can be tested with precision. Our results
show that the chemical potential weakens the heavy-quark deconfinement
transition in QCD.Comment: 6 pages and 7 figures. talk presented at Lattice 2005 (non-zero
temperature and density

### Testing Dimensional Reduction in SU(2) Gauge Theory

At high temperature, every $(d+1)$-dimensional theory can be reformulated as
an effective theory in $d$ dimensions. We test the numerical accuracy of this
Dimensional Reduction for (3+1)-dimensional SU(2) by comparing perturbatively
determined effective couplings with lattice results as the temperature is
progressively lowered. We observe an increasing disagreement between numerical
and perturbative values from $T=4 T_c$ downwards, which may however be due to
somewhat different implementations of dimensional reduction in the two cases.Comment: Lattice2001(hightemp), AMS-LaTeX v1.2, 3 pages with 3 figure

### Critical point in finite density lattice QCD by canonical approach

We propose a method to find the QCD critical point at finite density
calculating the canonical partition function ${\cal Z}_{\rm C} (T,N)$ by
Monte-Carlo simulations of lattice QCD, and analyze data obtained by a
simulation with two-flavor p4-improved staggered quarks with pion mass $m_{\pi}
\approx 770 {\rm MeV}$. It is found that the shape of an effective potential
changes gradually as the temperature decreases and a first order phase
transition appears in the low temperature and high density region. This result
strongly suggests the existence of the critical point in the $(T, \mu_q)$ phase
diagram.Comment: 4 pages, 2 figures, To appear in the conference proceedings for Quark
Matter 2009, March 30 - April 4, Knoxville, Tennesse

### Glueball masses in 4d U(1) lattice gauge theory using the multi-level algorithm

We take a new look at plaquette-plaquette correlators in 4d compact U(1)
lattice gauge theory which are separated in time, both in the confined and the
deconfined phases. From the behaviour of these correlators we extract glueball
masses in the scalar as well as the axial-vector channels. Also in the
deconfined phase, the non-zero momentum axial-vector correlator gives us
information about the photon which appears as a massless particle in the
spectrum. Using the Luescher - Weisz multi-level algorithm, we are able to go
to large time separations which were not possible previously.Comment: 18 pages, 7 figures and 3 tables. Minor notational change

### The isentropic equation of state of 2-flavor QCD

Using Taylor expansions of the pressure obtained previously in studies of
2-flavor QCD at non-zero chemical potential we calculate expansion coefficients
for the energy and entropy densities up to ${\cal O}(\mu_q^6)$ in the quark
chemical potential. We use these series in $\mu_q/T$ to determine lines of
constant entropy per baryon number ($S/N_B$) that characterize the expansion of
dense matter created in heavy ion collisions. In the high temperature regime
these lines are found to be well approximated by lines of constant $\mu_q/T$.
In the low temperature phase, however, the quark chemical potential is found to
increase with decreasing temperature. This is in accordance with resonance gas
model calculations. Along the lines of constant $S/N_B$ we calculate the energy
density and pressure. Within the accuracy of our present analysis we find that
the ratio $p/\epsilon$ for $T>T_0$ as well as the softest point of the equation
of state, $(p/\epsilon)_{min}\simeq 0.075$, show no significant dependence on
$S/N_B$.Comment: 7 pages, 10 figure

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