Polyakov Loop Susceptibilities Research Articles

Deconfinement of heavy quarks at finite density and strong magnetic field

We study the simultaneous effect of the external magnetic field and finite chemical potential on deconfinement of heavy quarks, probed by the Polyakov loop and its fluctuations. We calculate the Polyakov loop, its real and imaginary susceptibilities, their ratio, as well as the heavy quark and anti-quark entropies. We find that these quantities are sensitive probes of deconfinement. Especially, the real Polyakov loop susceptibility and heavy quark and anti-quark entropies diverge at the critical point.

Quark and Polyakov-loop correlations in effective models at zero and nonvanishing density

The aim of this work is to shed light on some lesser known aspects of Polyakov-loop--extended chiral models (namely the Polyakov-loop extended Nambu--Jona-Lasinio and Quark-Meson models), especially on the correlation of the quark sector with the Polyakov loop. We show that the ordering of chiral and Polyakov-loop transitions and their difference in temperature as seen in lattice QCD calculations could be realized with a critical scale of the Polyakov-loop potential that is larger than the one in pure gauge theory. The comparison of the results for the Polyakov-loop susceptibility obtained using the self-consistent medium-dependent quark mass with those obtained while keeping these masses at a fixed value allows to disentangle chiral-symmetry restoration and center-symmetry breaking effects. Furthermore, a confined chirally restored phase is identified by a plateau in the quark contribution to thermodynamics and by sigma and pion spectral functions that coincide but have a small width. We also discuss that, for some large chemical potential values, the explicit center-symmetry breaking is so strong that statistical deconfinement is realized at infinitely small temperatures. Both the missing sensitivity of the Polyakov loop to the quark mass, except at close to the chiral transition, and the Polyakov loop being zero at zero temperature at all chemical potentials, can be interpreted as indications of a missing mechanism which accounts for the quark back-reaction on the Polyakov loop.

Polyakov loop fluctuations in the presence of external fields

We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.

Polyakov loop effects on the phase diagram in strong-coupling lattice QCD

We investigate the Polyakov loop effects on the QCD phase diagram by using the strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one species of unrooted staggered quark, including O}(1/g^4) effects. We take account of the effects of Polyakov loop fluctuations in Weiss mean-field approximation (MFA), and compare the results with those in the Haar-measure MFA (no fluctuation from the mean-field). The Polyakov loops strongly suppress the chiral transition temperature in the second-order/crossover region at small chemical potential, while they give a minor modification of the first-order phase boundary at larger chemical potential. The Polyakov loops also account for a drastic increase of the interaction measure near the chiral phase transition. The chiral and Polyakov loop susceptibilities have their peaks close to each other in the second-order/crossover region. In particular in Weiss MFA, there is no indication of the separated deconfinement transition boundary from the chiral phase boundary at any chemical potential. We discuss the interplay between the chiral and deconfinement dynamics via the bare quark mass dependence of susceptibilities.

Single quark entropy and the Polyakov loop

We study Quantum Chromodynamics (QCD) with 2 + 1 flavors with almost physical quark masses using the highly improved staggered quark action (HISQ). We calculate the Polyakov loop in a wide temperature range, obtain the free energy and the entropy of a single static quark and discuss the QCD crossover region in detail. We show that the entropy has a peak close to the chiral crossover and consider the consequences for the deconfinement aspects of the crossover phenomena. We study the renormalized Polyakov loop susceptibilities and place them into the context of the crossover. We also obtain a quantitative result for the onset of weak-coupling behavior at high temperatures.

The Wilson flow and the finite temperature phase transition

We consider the determination of the finite temperature phase transition in the Yang--Mills SU(3) gauge theory. We compute the difference of the spatial and temporal energy density at a physical Wilson flow time. This difference is zero in the confined phase and becomes non zero in the deconfined phase. We locate the phase transition by using a new technique based on an exponential smoothing spline. This method is an alternative to the determination of the phase transition based on the Polyakov loop susceptibility and can also be used with dynamical fermions.

Polyakov loop in2+1flavor QCD from low to high temperatures

We study the free energy of a static quark in QCD with 2+1 flavors in a wide temperature region, 116 MeV $< T < $ 5814 MeV, using the highly improved staggered quark (HISQ) action. We analyze the transition region in detail, obtain the entropy of a static quark, show that it peaks at temperatures close to the chiral crossover temperature and also revisit the temperature dependence of the Polyakov loop susceptibilities using gradient flow. We discuss the implications of our findings for the deconfinement and chiral crossover phenomena at physical values of the quark masses. Finally a comparison of the lattice results at high temperatures with the weak-coupling calculations is presented.

Probing the QCD phase diagram with fluctuations

The relevance of higher order cumulants of conserved charges for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC is discussed. Using properties of $O(4)$ scaling functions, the generic structure of these higher cumulants at vanishing baryon chemical potential is discussed. Chiral model calculations are then used to study their properties at non-zero baryon chemical potential. It is argued that the rapid variation of sixth and higher order cumulants at the phase boundary may be used to explore the QCD phase diagram in experiment. Moreover, results for the Polyakov loop susceptibilities in SU(3) lattice gauge theory as well as in (2+1) flavor lattice QCD are discussed. An analysis of the ratios of susceptibilities indicates that the deconfinement transition is reflected in characteristic modifications of these ratios.

Polyakov loop susceptibilities in pure gauge system

We present new lattice results on Polyakov loop susceptibilities in the SU(3) pure gauge system. Ratios of these susceptibilities are useful probes for deconfinement. Progress toward understanding these ratios in the presence of quarks are briefly discussed.

Probing Deconfinement with Polyakov Loop Susceptibilities

Probing Deconfinement with Polyakov Loop Susceptibilities

SU(3) deconfining phase transition with finite volume corrections due to a confined exterior

Using the geometry of a double-layered torus we investigate the deconfining phase transition of pure SU(3) lattice gauge theory by Markov chain Monte Carlo simulations. In one layer, called "outside", the temperature is set below the deconfining temperature and in the other, called "inside", it is iterated to a pseudo-transition temperature. Lattice sizes are chosen in a range suggested by the physical volumes achieved in relativistic heavy ion collisions and both temperatures are kept close enough to stay in the SU(3) scaling region. Properties of the transition are studied as function of the volume for three outside temperatures. When compared with infinite volume extrapolations, small volume corrections of the deconfining temperature and width become competitive with those found by including quarks. Effective finite size scaling exponents of the specific and Polyakov loop susceptibilities are also calculated.

Polyakov loop fluctuations in SU(3) lattice gauge theory and an effective gluon potential

We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctuations of the Polyakov loop, as well as that of its absolute value, are considered. We analyze their properties in relation to the confinement-deconfinement phase transition. We also present results based on simulations of ($2+1$)-flavor QCD on ${32}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice using highly improved staggered quark action by the HotQCD collaboration. The influences of fermions on the Polyakov loop fluctuations are discussed. We show that ratios of different susceptibilities of the Polyakov loop are sensitive probes for critical behavior. We formulate an effective model for the Polyakov loop potential and constrain its parameters from existing quenched lattice data including fluctuations. We emphasize the role of fluctuations to fully explore the thermodynamics of pure gauge theory within an effective approach.

Probing deconfinement with Polyakov loop susceptibilities

The susceptibilities of the real and imaginary parts, as well as of the modulus, of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent of the renormalization of the Polyakov loop and only weakly dependent on the system size. The ratios are almost temperature independent above and below the transition and exhibit a discontinuity at the transition temperature. This characteristic behavior can be understood in terms of the global ${\mathcal{Z}}_{3}$ symmetry of the Yang-Mills Lagrangian and the general properties of the Polyakov loop probability distribution.

The deconfinement transition of finite density QCD with heavy quarks from strong coupling series

Starting from Wilson's action, we calculate strong coupling series for the Polyakov loop susceptibility in lattice gauge theories for various small N_\tau in the thermodynamic limit. Analysing the series with Pad\'e approximants, we estimate critical couplings and exponents for the deconfinement phase transition. For SU(2) pure gauge theory our results agree with those from Monte-Carlo simulations within errors, which for the coarser N_\tau=1,2 lattices are at the percent level. For QCD we include dynamical fermions via a hopping parameter expansion. On a N_\tau=1 lattice with N_f=1,2,3, we locate the second order critical point where the deconfinement transition turns into a crossover. We furthermore determine the behaviour of the critical parameters with finite chemical potential and find the first order region to shrink with growing \mu. Our series moreover correctly reflects the known Z(N) transition at imaginary chemical potential.

Finite temperature phase transition in full QCD with Nf = 2 flavors of clover fermions at Nf = 8 and 10

We present results for QCD with $N_f=2$ flavors of dynamical quarks using nonperturbatively improved Wilson fermions at finite temperature on $16^3 \times 8$ and $24^3 \times 10$ lattices. We determine the transition temperature in the range of quark masses $0.6 \lesssim m_\pi/m_\rho \leq 0.8$. After fixing the Maximal Abelian gauge we investigate the contribution of Abelian monopoles to the Polyakov loop, Polyakov loop susceptibility and confirm Abelian and monopole dominance in full QCD.

Deconfinement through chiral transition in 2 flavour QCD

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T χ and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behavior of Polyakov loop susceptibilities at T χ is shown to be supported by finite temperature lattice calculations.

Deconfinement through chiral symmetry restoration in two-flavour QCD

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T-chi and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at T-chi is shown to be supported by finite temperature lattice calculations.

Phase structure of one-flavour QCD

Abstract Phase structure of one-flavour QCD C. Alexanch-ou a, 1, A. Borici b, A. Feo a, Ph. de Forcrand c, A. Galli d, F. Jegerlehner e, T. Takaishi f a Department of Natural Sciences, Unh,ersity of Cyprns, CY-1678 Nicosia, Cypnls b Paul Scherrer Institute, CH-5232 Villigen, Switzerland c Swiss Center for Scientific Computing, ETH-Zentnml, CH-8092 Ziirich, Switzerland d ELCA b~formatique, Hofiviesen Str. 26, CH-8057 Ziirich, Switzerland e DESY-IfH Zeuthen, D-15738 Zeuthen, Germany f Hiroshbna University of Economics, 731-01 Hiroshhna, Japan We present a study of the deconfinement phase transition of one-flavour QCD, using the multiboson algorithm [1]. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson algorithm [2] is a very suitable simulation algorithm. Finite size scaling is studied on lattices of size 83 x 4, 123 x 4 and 163 x 4. For heavy quarks, the behaviour of observables that probe the phase change, such as the Polyakov loop susceptibility, transition. The first-order transition weakens as the quark mass decreases and turns into a crossover. Locating the end-point (/~ep,/¢ep) accurately requires very large lattice sizes, beyond our computer capabilities. We thus consider an effective model, in the same universality class as full QCD but cheaper to simulate. By simulating larger systems, we locate the end-point in the coupling plane of this model. Then we map this end-point back onto full QCD. We thus estimate the end point of the first-order phase transition to occur at a quark mass of about 1.4 GeV. © 1999 Elsevier Science B.V. All rights reserved.

Deconfinement phase transition in one-flavor QCD

We present a study of the deconfinement phase transition of one-flavor QCD using the multiboson algorithm. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson method is a superior simulation algorithm. Finite-size scaling is studied on lattices of size ${8}^{3}\ifmmode\times\else\texttimes\fi{}4,$ ${12}^{3}\ifmmode\times\else\texttimes\fi{}4$, and ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$. The behaviors of the peak of the Polyakov loop susceptibility, the deconfinement ratio, and the distribution of the norm of the Polyakov loop are all characteristic of a first-order phase transition for heavy quarks. As the quark mass decreases, the first-order transition gets weaker and turns into a crossover. To investigate finite-size scaling on larger spatial lattices we use an effective action in the same universality class as QCD. This effective action is constructed by replacing the fermionic determinant with the Polyakov loop identified as the most relevant $Z(3)$-symmetry-breaking term. Higher-order effects are incorporated in an effective $Z(3)$-breaking field h, which couples to the Polyakov loop. Finite-size scaling determines the value of h where the first-order transition ends. Our analysis at the end point ${h}_{\mathrm{ep}}$ indicates that the effective model and thus QCD are consistent with the universality class of the three-dimensional Ising model. Matching the field strength at the end point ${h}_{\mathrm{ep}}$ to the $\ensuremath{\kappa}$ values used in the dynamical quark simulations we estimate the end point ${\ensuremath{\kappa}}_{\mathrm{ep}}$ of the first-order phase transition. We find ${\ensuremath{\kappa}}_{\mathrm{ep}}\ensuremath{\sim}0.08$ which corresponds to a quark mass of about 1.4 GeV.

Thermodynamics of two-colour QCD

We discuss the thermodynamics of two-colour QCD with four flavours of staggered quarks on 8 3 × 4 and 16 3 × 4 lattices. In our simulations we use the Naik action for the fermions and a (1,2) tree-level improved gauge action. We analyze the deconfinement and chiral phase transitions for four different quark masses (m=0.1,0.05,0.025,0.015). Contrary to three-colour QCD the peak in the Polyakov loop susceptibility decreases with decreasing quark mass. This reflects an early breaking of the string in the heavy quark potential, which we verify explicitly by calculating the heavy quark potential at finite temperature using Polyakov loop correlations.