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In June 2004 QCD was simulated for the first time at sustained speed exceeding 1 TeraFlops in the BlueGene/L supercomputer at the IBM T.J. Watson Research Lab. The implementation and performance of QCD in the BlueGene/L is presented., Talk presented at Lattice2004(machines), Fermilab, 21-26 June 2004, 3 pages, 5 figures

High performance computers are reviewed. Specially built dedicated machines from APE, Columbia, CP-PACS, and RTNN are described. We also consider recent developments in the commercial computer world, and compare machine performances and costs per sustained Gigaflop.

We study the quenched and unquenched lattice Schwinger model with Wilson fermions. The lowest non-trivial order of the systematic expansion recently proposed by Sexton and Weingarten is shown to allow good estimates of long distance physics from quenched configurations. Results for the static potential and the lowest bound state mass are presented.

We discuss a class of reversible, discrete approximations to Hamilton's equations for use in the hybrid Monte Carlo algorithm and derive an asymptotic formula for the step-size-dependent errors arising from this family of approximations. For lattice QCD with Wilson fermions, we construct several different updates in which the effect of fermion vacuum polarization is given a longer time step than the gauge field's self-interaction. On a 44 lattice, one of these algorithms with an optimal choice of step size is 30% to 40% faster than the standard leapfrog update with an optimal step size.

We describe a new geometrical discretisation method which exactly preserved topological properties of U(1) Chern-Simons theories. A numerical calculation using these new methods correctly evaluates the Reidemeister Torsion for low order Lens spaces.

We evaluate the coupling constant for the lightest scalar glueball to decay to pseudoscalar meson pairs. The calculation is done in the valence approximation on a $16^3 \times 24$ lattice at $\beta = 5.70$ for two different values of pseudoscalar meson mass., Comment: 3 pages, Latex, 1 PostScript figure, requires espcrc2.tex, espcrc2.sty neither of which is included, talk at Lat94

We describe plans for a parallel computer composed of 16K nodes interconnected in a 16 3 × 4 mesh. Each node is made up of a Texas Instruments TMS320C31 digital signal processor, 0.5M words of error-corrected memory and a gate array providing memory management and inter-node communication. The machine will have a peak speed of 0.8Tflops and is estimated to sustain ≈ 0.5Tflops for lattices as small as 32 3 × 8. We plan to complete the machine within two years for a cost of $3M.

PUBLISHED, A scheme for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo (HMC) simulations of gauge theories with dynamical fermions is presented. The algorithm is tested in the Schwinger model with Wilson fermions., MP is grateful to Enterprise-Ireland for support under grant SC/01/306.

We present hadron mass spectrum results for valence Wilson fermions obtained from simulations on the GF11. We performed high statistic runs on three physical volumes, 8 3 × 32, 16 3 × 32, and 24 3 × 32, all with the same coarse lattice spacing, β = 5.7. We see no systematic difference between our 8 3 and 16 3 results at the large quark masses we could simulate on 8 3 . Our 16 3 and 24 3 results also agree at the small quark masses we simulated on these larger volumes.

Recent developments and applications of approximate actions for full lattice QCD are described. We present first results based on the stochastic estimation of the fermion determinant on $12^3\times 24$ configurations at $\beta=5.2$., Comment: 3 pages, Latex, no figures, Contribution to Lattice 97, The XV International Symposium on Lattice Field Theory, Edinburgh 22-26 July 1997

We evaluate the partial decay widths of the lightest scalar glueball to pairs of pseudoscalar quark-antiquark states. The calculation is done in the valence (quenched) approximation on a $16^3 \time 24$ lattice at $\beta = 5.7$. These predictions and values obtained earlier for the infinite volume continuum limit of the scalar glueball's mass are in good agreement with the observed properties of $f_J(1710)$ and inconsistent with all other observed meson resonances., Comment: 8 pages of Latex, 12 PostScript figures, 2 macros included, plenary talk given by D. Weingarten at Lattice 95, to appear in conference proceedings

The first stage in the construction of the 0.8 Teraflops Supercomputer at Columbia, a working, two node parallel computer, has been successfully completed. The next stage, a 512 node, 26 Gigaflops prototype, is in its final construction phase. A general description and current status of the hardware and software is presented., 4 pages, uuencoded compressed Postscript file, contribution to Lattice 95

We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included., 3 pages, latex, no figures, requires espcrc2.sty (included at end) Contribution to Lattice 94 proceedings

We obtain estimates of several hadron mass ratios, for Wilson quarks in the valence (quenched) approximation, extrapolated to physical quark mass, infinite volume and zero lattice spacing., 10 pages of Latex + 2 PostScript files attached

The install and debug phase for GF11's hardware is rapidly approaching completion. The system software is also almost complete. Currently both are quite stable and quite usable. The remaining installation is straight forward and should be complete in a few more months. The so far successful installation and testing have shown GF11 to be a viable system. Indeed it seems that the architecture is such that achieving over 80% usage of the machine's peak speed for typical QCD lattice calculations is a realistic goal. This is a very impressive number and bodes well for GF11's ability to tackle the physics problems it will almost immediately be facing.

A new method to analytically determine the partition function zeroes of weakly coupled theories on finite-size lattices is developed. Applied to the lattice Schwinger model, this reveals the possible absence of a phase transition at fixed weak coupling. We show how finite-size scaling techniques on small or moderate lattice sizes may mimic the presence of a spurious phase transition. Application of our method to the Gross-Neveu model yields a phase diagram consistent with that coming from a saddle point analysis., Talk at LATTICE99, 3 pages, 2 figures