Phase Structure Of Lattice QCD Research Articles

Critical point search from an extended parameter space of lattice QCD at finite temperature and density

Aiming to understand the phase structure of lattice QCD at nonzero temperature and density, we study the phase transitions of QCD in an extended parameter space, where the number of flavor and quark masses are considered as parameters. Performing simulations of 2 flavor QCD and using the reweighting method, we investigate (2+Nf) flavor QCD at finite density, where two light flavors and Nf massive flavors exist. Calculating probability distribution functions, we determine the critical surface terminating first order phase transitions in the parameter space of the light quark mass, the heavy quark mass and the chemical potential. Through the study of the many flavor system, we discuss the phase structure of QCD at finite density.

Histograms in heavy-quark QCD at finite temperature and density

We study the phase structure of lattice QCD with heavy quarks at finite temperature and density by a histogram method. We determine the location of the critical point at which the first-order deconfining transition in the heavy-quark limit turns into a crossover at intermediate quark masses through a change of the shape of the histogram under variation of coupling parameters. We estimate the effect of the complex phase factor, which causes the sign problem at finite density, and show that, in heavy-quark QCD, the effect is small around the critical point. We determine the critical surface in $2+1$ flavor QCD in the heavy-quark region at all values of the chemical potential $\ensuremath{\mu}$ including $\ensuremath{\mu}=\ensuremath{\infty}$.

Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential

We present results for phase structure of lattice QCD with two degenerate flavors (${N}_{f}=2$) of Wilson quarks at finite temperature $T$ and small baryon chemical potential ${\ensuremath{\mu}}_{B}$. Using the imaginary chemical potential for which the fermion determinant is positive, we perform simulations at points where the ratios of pseudoscalar meson mass to the vector meson mass ${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}$ are between 0.943(3) and 0.899(4) as well as in the quenched limit. By analytic continuation to real quark chemical potential $\ensuremath{\mu}$, we obtain the transition temperature as a function of small ${\ensuremath{\mu}}_{B}$. We attempt to determine the nature of transition at imaginary chemical potential by histogram, Monte Carlo (MC) history, and finite size scaling. In the infinite heavy quark limit, the transition is of first order. At intermediate values of quark mass ${m}_{q}$ corresponding to the ratio of ${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}$ in the range from 0.943(3) to 0.899(4) at $a{\ensuremath{\mu}}_{I}=0.24$, the MC simulations show the absence of phase transition.

Lattice spacing dependence of the first order phase transition for dynamical twisted mass fermions

Lattice QCD with Wilson fermions generically shows the phenomenon of a first order phase transition. We study the phase structure of lattice QCD using Wilson twisted mass fermions and the Wilson plaquette gauge action in a range of β values where such a first order phase transition is observed. In particular, we investigate the dependence of the first order phase transition on the value of the lattice spacing. Using only data in one phase and neglecting possible problems arising from the phase transition we are able to perform a first scaling test for physical quantities using this action.

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.

Twisted mass quarks and the phase structure of lattice QCD

The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable in correspondence of which the untwisted quark mass assumes positive or negative values. We provide interpretations of this phenomenon in terms of chiral symmetry breaking and the effective potential model of Sharpe and Singleton.

Exploring the phase structure of lattice QCD with twisted mass quarks

The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable when the untwisted quark mass sweeps across zero.

Phase structure of lattice QCD for general number of flavors

We investigate the phase structure of lattice QCD for the general number of flavors in the parameter space of gauge coupling constant and quark mass, employing the one-plaquette gauge action and the standard Wilson quark action. Performing a series of simulations for the number of flavors $N_F=6$--360 with degenerate-mass quarks, we find that when $N_F \ge 7$ there is a line of a bulk first order phase transition between the confined phase and a deconfined phase at a finite current quark mass in the strong coupling region and the intermediate coupling region. The massless quark line exists only in the deconfined phase. Based on these numerical results in the strong coupling limit and in the intermediate coupling region, we propose the following phase structure, depending on the number of flavors whose masses are less than $\Lambda_d$ which is the physical scale characterizing the phase transition in the weak coupling region: When $N_F \ge 17$, there is only a trivial IR fixed point and therefore the theory in the continuum limit is free. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial IR fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$.

Phase structure of lattice QCD at finite temperature for 2+1 flavors of Kogut-Susskind quarks

We report on a study of the finite-temperature chiral transition on an N t = 4 lattice for 2 + 1 flavors of Kogut-Susskind quarks. We find the point of physical quark masses to lie in the region of crossover, in agreement with results of previous studies. Results of a detailed examination of the m u,d = m s case indicate vanishing of the screening mass of σ meson at the end point of the first-order transition.

Phase structure of lattice QCD with Wilson fermion at finite temperature

We review our attempt at understanding the phase structure of lattice QCD with the Wilson fermion formulation at finite temperature, based on a spontaneous breakdown of parity-flavor symmetry. Numerical results demonstrating explicitly the spontaneous breakdown of parity-flavor symmetry beyond the critical line at both zero and finite temperatures are reported. The phase structure and order of the chiral transition are reported for $N_f=2$,3, and 4 flavors, and the approach towards the continuum limit is discussed.

Quantum Chromodynamics with Many Flavors

We investigate the phase structure of lattice QCD for general number of flavors $N_F$. Based on numerical data combined with the results of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only one IR fixed point at vanishing gauge coupling, i.e., the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point. Therefore, the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$.

Finite-temperature phase structure of lattice QCD with the Wilson quark action for two and four flavors

We present further analyses of the finite-temperature phase structure of lattice QCD with the Wilson quark action based on spontaneous breakdown of parity-flavor symmetry. Results are reported on (i) an explicit demonstration of spontaneous breakdown of parity-flavor symmetry beyond the critical line, (ii) phase structure and order of chiral transition for the case of N f = 4 flavors, and (iii) approach toward the continuum limit.

Phase structure of lattice QCD at finite density with dynamical fermions

We compare the chemical potential associated with the onset of non-zero baryon number density on 6 4 and 8 4 lattices at β = 5.1 and ma = 0.01. We provide evidence for Z(3) tunnelling. We determine a critical chemical potential of μ a ≅ 0.1 which is unexpectedly low. We also determine the dependence of the onset of the observed phase transition on the quark mass. The physically misleading result of the quenched theory is shown to persist despite the inclusion of the complex fermion determinant.

Fate of the critical line and chiral transition in finite-temperature lattice QCD with the Wilson quark action

Finite-temperature phase structure of lattice QCD with the Wilson quark action is analyzed. We show that the critical line at finite temperatures, defined to be the line of vanishing pion screening mass, turns back toward strong coupling, forming a cusp on the ( β , K ) plane, and that the line of thermal transition runs past the tip of the cusp without touching the critical line. Previous results are discussed in the light of our findings.

Finite-temperature phase structure of lattice QCD with Wilson quark action.

The long-standing issue of the nature of the critical line of lattice QCD with the Wilson quark action at finite-temperatures, defined to be the line of vanishing pion screening mass, and its relation to the line of finite-temperature chiral tansition is examined. Analytical and numerical evidence are presented that the critical line forms a cusp at a finite gauge coupling, and the line of chiral transition runs past the tip of the cusp without touching the critical line. Implications on the continuum limit and the flavor dependence of chiral transition are discussed.

On the Phase Structure of QCD with Wilson Fermions

The phase structure of lattice QCD with Wilson fermions is discussed. Analytic and numerical evidences are given for the spontaneous breaking of parity and flavor symmetry, which naturally explains the existence of the massless pion at the critical hopping parameter $K_c$ without recourse to the chiral symmetry absent in the Wilson fermion formulation. New numerical evidences are also presented for the multiple structure of the critical lines in the weak coupling region. A connection between the phase structure and the finite temperature phase transition is briefly mentioned.

Finite-temperature phase structure of lattice QCD for 8 and 17 flavors.

The finite-temperature phase structure of lattice quantum chromodynamics with ${N}_{f}=8 \mathrm{and} 17$ flavors of staggered quarks is mapped out in the range of quark mass $0.1\ensuremath{\le}{m}_{q}a\ensuremath{\le}10$ on the ${16}^{3}$\ifmmode\times\else\texttimes\fi{}4 lattice and at zero baryon density. In contrast with an earlier study, chiral and deconfinement phase transitions are found to correspond to separate domains on the (${m}_{q}$, ${N}_{f}$) plane. No qualitative difference is found between the phase structures for the two values of ${N}_{f}$, nor between the two and the one for ${N}_{f}=4$. The chiral transition is found to strengthen with increasing ${N}_{f}$.

Wilson fermions on the lattice—A study of the eigenvalue spectrum

We have studied the eigenvalues of the Wilson fermion matrix on various lattice sizes and for a range of coupling constants, β, in the quenched approximation. The implications for the phase structure of lattice QCD in the presence of Wilson fermions are discussed.

Phase structure of lattice QCD including virtual quark loops

Phase structure of lattice QCD including virtual quark loops