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 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

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

The canonical approach to Finite Density QCD

We present a canonical approach to study properties of QCD at finite baryon density rho, and apply it to the determination of the phase diagram of four-flavour QCD. For a pion mass of about 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. We obtain accurate results for systems containing up to 30 baryons and quark chemical potentials mu up to 2T. Our T-mu phase diagram agrees with the literature when mu/T < 1. At larger chemical potential, we observe a ``bending down'' of the phase boundary. We characterise the two phases with simple models: the hadron resonance gas in the hadronic phase, the free massless quark gas in the plasma phase.Comment: 6 pages, 8 figures, talk presented at Lattice 2005 (Non-zero temperature and density

String breaking with Wilson loops?

A convincing, uncontroversial observation of string breaking, when the static potential is extracted from Wilson loops only, is still missing. This failure can be understood if the overlap of the Wilson loop with the broken string is exponentially small. In that case, the broken string ground state will only be seen if the Wilson loop is long enough. Our preliminary results show string breaking in the context of the 3d SU(2) adjoint static potential, using the L\"uscher-Weisz exponential variance reduction approach. As a by-product, we measure the fundamental SU(2) static potential with improved accuracy and see clear deviations from Casimir scaling.Comment: Lattice2002(topology), AMS-LaTeX v1.2, 3 pages with 2 figures; added reference

Observing string breaking with Wilson loops

An uncontroversial observation of adjoint string breaking is proposed, while measuring the static potential from Wilson loops only. The overlap of the Wilson loop with the broken-string state is small, but non-vanishing, so that the broken-string groundstate can be seen if the Wilson loop is long enough. We demonstrate this in the context of the (2+1)d SU(2) adjoint static potential, using an improved version of the Luscher-Weisz exponential variance reduction. To complete the picture we perform the more usual multichannel analysis with two basis states, the unbroken-string state and the broken-string state (two so-called gluelumps). As by-products, we obtain the temperature-dependent static potential measured from Polyakov loop correlations, and the fundamental SU(2) static potential with improved accuracy. Comparing the latter with the adjoint potential, we see clear deviations from Casimir scaling.Comment: 35 pages, 12 figures. 1 reference adde