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The magnitude of the $U_A(1)$ symmetry breaking is expected to affect the nature of $N_f=2$ QCD chiral phase transition. The explicit breaking of chiral symmetry due to realistic light quark mass is small, so it is important to use chiral fermions on the lattice to understand the effect of $U_A(1)$ near the chiral crossover temperature, $T_c$. We report our latest results for the eigenvalue spectrum of 2+1 flavour QCD with dynamical Mobius domain wall fermions at finite temperature probed using the overlap operator on $32^3\times 8$ lattice. We check how sensitive the low-lying eigenvalues are to the sea-light quark mass. We also present a comparison with the earlier independent results with domain wall fermions., 7 pages, 6 Figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, Kobe, Japan

We investigate the low-lying eigenmodes of the Dirac matrix with the aim to gain more insight into the temperature dependence of the anomalous $U_A(1)$ symmetry. We use the overlap operator to probe dynamical QCD configurations generated with (2+1)-flavors of highly improved staggered quarks. We find no evidence of a gap opening up in the infrared region of the eigenvalue spectrum even at $1.5\,T_c$, $T_c$ being the chiral crossover temperature. Instead, we observe an accumulation of near-zero eigenmodes. We argue that these near-zero eigenmodes are primarily responsible for the anomalous breaking of the axial symmetry still being effective. At $1.5\,T_c$, these near-zero eigenmodes remain localized and their distribution is consistent with the dilute instanton gas picture. At this temperature, the average size of the instantons is $0.223(8)\,\text{fm}$ and their density is $0.147(7)\,\text{fm}^{-4}$., Comment: 15 pages, 19 figures

QCD with four dynamical flavours of staggered quarks has been simulated on a 163 x 24 lattice at β = 5.35 and ma = 0.01. Some results on the hadron spectrum, on the chiral condensate and the confinement as well as the spin-dependent heavy quark potential are presented.

The Hypercube operator determines a variant of the approximate, truncated perfect fermion action. In this pilot study we are going to report on first experiences in dynamical QCD simulations with the Hypercube fermions. We apply this formulation in an investigation of the finite temperature transition for two flavours. On lattices of size $8^3\times 4$ we explore the phase diagram. Physical scales are estimated from pseudoscalar and vector meson masses obtained on $8^3\times 16$ lattices. We observe the presence of a metastability region but do not find evidence for an Aoki phase. The Hypercube operator allows us to simulate at ratios of pseudoscalar to vector meson masses at least as small as 0.8 at the thermal crossover at $N_t=4$, which renders this formulation cheaper than the Wilson like fermions., 7 pages, 8 figures, talk presented at Lattice 2006 (High temperature and density)

We determine the location of the second order endpoint of the line of first order chiral phase transition in 3-flavor QCD at vanishing chemical potential. Using Ferrenberg-Swendsen reweighting for two values of the quark mass we determine the dependence of the transition line on the chemical potential and locate the chiral critical point. For both quantities we find a significant quark mass dependence.

The article presents a selected set of recent results from numerical investigations of QCD at finite temperature. It is focused (i) on the present understanding of thermodynamic properties of QCD in the presence of dynamical quarks at various masses and at small yet phenomenologically relevant values for the baryon density and (ii) on a fairly new approach to studying thermal hadronic excitations.

We discuss the non-zero baryon number formulation of QCD in the quenched limit at finite temperature. This describes the thermodynamics of gluons in the background of static quark sources. Although a sign problem remains in this theory, our simulation results show that it can be handled quite well numerically. The transition region gets shifted to smaller temperatures and the transition region broadens with increasing baryon number. Although the action is in our formulation explicitly Z(3) symmetric the Polyakov loop expectation value becomes non-zero already in the low temperature phase and the heavy quark potential gets screened at non-vanishing number density already this phase., LATTICE99(Finite Temperature and Density), Latex2e using espcrc2.sty, 3 pages, 7 figures

It has been proposed, that the chiral continuum limit of 2-flavour QCD with Wilson fermions is brought about by a phase in which flavour and parity symmetry are broken spontaneously at finite lattice spacing. At finite temperature this phase should retract from the weak coupling limit to form 5 cusps. This scenario is studied with tree level Symanzik improved actions for both gauge and fermion fields on lattices of size $8^3\times 4$ and $12^2\times 24\times 4$., Comment: Talk given at Conference on Strong and Electroweak Matter (SEWM 98), Copenhagen, Denmark, 2-5 Dec 1998

We discuss the quenched limit of lattice QCD at non-zero baryon number density. We find evidence for a mixed phase that becomes broader with increasing baryon number. Although the action is explicitly Z(3) symmetric the Polyakov loop expectation value becomes non-zero already in the low temperature phase. It indicates that the heavy quark potential stays finite at large distances, i.e. the string between static quarks breaks at non-zero baryon number density already in the hadronic phase. This behaviour is validated by calculating the heavy quark potential using Polyakov loop correlations., Comment: 6 pages, 6 figures, talk presented at ``Understanding Deconfinement in QCD'', ECT* Trento, March 1999

The quark–gluon plasma (QGP), the deconfined high-temperature phase of QCD, is currently under extensive investigation in heavy-ion collision experiments at RHIC and LHC. The transition from the hadronic, low-temperature phase to the QGP is a rapid crossover, manifested by a significant change in bulk thermodynamic quantities. A fundamental characteristics of QCD is the equation of state, which is also an essential ingredient of hydrodynamic modeling of heavy-ion collisions. We report our final result [1] for the 2 + 1 flavor QCD equation of state in the continuum limit. We calculate the pressure, energy density and other thermodynamic quantities in the experimentally relevant temperature range 130–400 MeV. We use the highly improved staggered quark (HISQ) action with the Goldstone pion mass tuned to about 160 MeV in the continuum limit. To perform the continuum extrapolation we use lattices with temporal extent N τ = 6 , 8 , 10 and 12 .

Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by performing lattice simulations in EQCD. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The finite chemical potential results are optained using analytic continuation. The diagonal susceptibility approaches the perturbative result above 20T_c$, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c. Hyvin korkeassa lämpötilassa ydinaine hajoaa pienimpiin rakenneosiinsa kvarkeiksi ja gluoneiksi. Tämä olomuodonmuutos aineen, jossa hiukkaset ovat sitoutuneet toisiinsa, ja uuden olomuodon kvarkkiguoniplasman välillä tapahtuu vasta erittäin korkeassa 10^12 Kelvinin lämpötilassa. Kvarkkigluoniplasman tutkimus on tällä hetkellä erittäin mielenkiintoisessa tilassa, sillä vasta aivan viime vuosina on tullut mahdolliseksi tutkia sitä kokeellisesti hiukkaskiihdyttimillä törmäyttämällä lähes valonnopeudella liikkuvia raskaita ioneita. Teoreettisesti tällaisen äärimmäisen kuuman vahvasti vuorovaikuttavan aineen ominaisuuksia kuvaa äärellisen lämpötilan kvanttikromodynamiikka. Kvarkkigluoniplasman tutkiminen on yksi keskeisimpiä teoreettisen hiukkasfysiikan tutkimuskohteita. Tässä väitöstutkimuksessa kvarkkigluoniplasman termodynaamisia ominaisuuksia on tutkittu hilasimulaatioiden avulla. Hilasimulaatiot ovat häiriöteorian lisäksi sekä lupaavin että laajimmin käytetty menetelmä vahvasti vuorovaikuttavan aineen tutkimuksessa. Lähtökohtana on ollut käyttää alkuperäistä teoriaa yksinkertaisempaa dimensionaalisesti pelkistettyä kolmiulotteista kenttäteoriaa. Tämä mahdollistaa perinteisiä hilasimulaatioita korkeampien lämpötilojen tutkimisen. Merkittävimpiä tuloksia ovat olleet paineen häiriöteorian ensimmäisen ei analyyttisen osan laskeminen ja kvarkkisuskeptibiliteetien tutkiminen. Kvarkkisuskeptibiliteetin tulokset sopivat hyvin sekä matalan lämpötilan hilatuloksiin että korkean lämpötilan häiriöteoreettisiin laskuihin ja näin ollen täydentävät ymmärtämystämme kvarkkisuskeptibiliteettien käytöksestä.