Lattice QCD Thermodynamics on the Grid

We describe how we have used simultaneously ${\cal O}(10^3)$ nodes of the EGEE Grid, accumulating ca. 300 CPU-years in 2-3 months, to determine an important property of Quantum Chromodynamics. We explain how Grid resources were exploited efficiently and with ease, using user-level overlay based on Ganga and DIANE tools above standard Grid software stack. Application-specific scheduling and resource selection based on simple but powerful heuristics allowed to improve efficiency of the processing to obtain desired scientific results by a specified deadline. This is also a demonstration of combined use of supercomputers, to calculate the initial state of the QCD system, and Grids, to perform the subsequent massively distributed simulations. The QCD simulation was performed on a $16^3\times 4$ lattice. Keeping the strange quark mass at its physical value, we reduced the masses of the up and down quarks until, under an increase of temperature, the system underwent a second-order phase transition to a quark-gluon plasma. Then we measured the response of this system to an increase in the quark density. We find that the transition is smoothened rather than sharpened. If confirmed on a finer lattice, this finding makes it unlikely for ongoing experimental searches to find a QCD critical point at small chemical potential

Laplacian gauge and instantons

We exhibit the connection between local gauge singularities in the Laplacian gauge and topological charge, which opens the possibility of studying instanton excitations without cooling. We describe our version of Laplacian gauge-fixing for SU(N).Comment: Lattice 2000 (Topology and Vacuum), 4 pages, 3 figures -- cosmetic change

Vortex free energies in SO(3) and SU(2) lattice gauge theory

Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).Comment: 3 pages, 2 figures, talk presented at Lattice2002(topology

Towards a controlled study of the QCD critical point

The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents the application of standard Monte Carlo techniques at non-zero baryon density. We have been pursuing an approach free of the sign problem, where the chemical potential is taken as imaginary and the results are Taylor-expanded in mu/T about mu=0, then analytically continued to real mu. Within this approach we have determined the sensitivity of the critical chemical potential mu_E to the quark mass, d(\mu_E)^2/dm_q|_{\mu_E=0}. Our study indicates that the critical point moves to {\em smaller} chemical potential as the quark mass {\em increases}. This finding, contrary to common wisdom, implies that the deconfinement crossover, which takes place in QCD at mu=0 when the temperature is raised, will remain a crossover in the mu-region where our Taylor expansion can be trusted. If this result, obtained on a coarse lattice, is confirmed by simulations on finer lattices now in progress, then we predict that no {\em chiral} critical point will be found for mu_B \lesssim 500 MeV, unless the phase diagram contains additional transitions.Comment: 4 pages, 6 figures, proceedings of Quark Matter 2008, Jaipur (India), Feb. 2008, to appear in J. Phys.

Electric and Magnetic Fluxes in SU(2) Yang-Mills Theory

We measure the free energies in SU(2) of static fundamental charges and center monopoles. Dual to temporal center fluxes, the former provide a well-defined (dis)order parameter for deconfinement. In contrast, the monopole free energies vanish in the thermodynamic limit at all temperatures and are thus irrelevant for the transition.Comment: 3 pages, LaTeX2e (espcrc2.sty), 4 figures (epsfig), for Lattice2002(topology

't Hooft loops and consistent order parameters for confinement

We study ratios of partition functions in two types of sectors of SU(2), with fixed temporal center flux and with static fundamental charge. Both can be used as bona fide order parameters for the deconfinement transition.Comment: 3 Pages, LaTeX 2.09 with espcrc2.sty, 4 Figures (epsfig), for Lattice2001(confinement

Localization properties of fermions and bosons

The topological structure of the QCD vacuum can be probed by monitoring the spatial localization of the low-lying Dirac eigenmodes. This approach can be pursued on the lattice, and unlike the traditional one requires no smoothing of the gauge field. I review recent lattice studies, attempting to extract a consistent description. What emerges is a picture of the vacuum as a ``topological sandwich'' of alternating, infinitely thin 3d layers of opposite topological charge, as originally seen in direct measurements of the topological charge density.Comment: Invited talk at "Quark Confinement and the Hadron Spectrum VII", Azores, Portugal, 2-7 September 2006. 7 pages, 11 figures. To appear in the Proceedings. Small changes; references adde

Fast Fermion Monte Carlo

Three possibilities to speed up the Hybrid Monte Carlo algorithm are investigated. Changing the step-size adaptively brings no practical gain. On the other hand, substantial improvements result from using an approximate Hamiltonian or a preconditioned action.Comment: Talk presented at LATTICE96(algorithms), 3 page