Finite-Size Effects in Lattice QCD with Dynamical Wilson Fermions

As computing resources are limited, choosing the parameters for a full Lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible. Aiming to push unquenched simulations with the Wilson action towards the computationally expensive regime of small quark masses we address the question whether one can possibly save computing time by extrapolating results from small lattices to the infinite volume, prior to the usual chiral and continuum extrapolations. In the present work the systematic volume dependence of simulated pion and nucleon masses is investigated and compared with a long-standing analytic formula by Luescher and with results from Chiral Perturbation Theory. We analyze data from Hybrid Monte Carlo simulations with the standard (unimproved) two-flavor Wilson action at two different lattice spacings of a=0.08fm and 0.13fm. The quark masses considered correspond to approximately 85 and 50% (at the smaller a) and 36% (at the larger a) of the strange quark mass. At each quark mass we study at least three different lattices with L/a=10 to 24 sites in the spatial directions (L=0.85-2.08fm).Comment: 21 pages, 20 figures, REVTeX 4; v2: caption of Fig.7 corrected, one reference adde

Improving the dynamical overlap algorithm

We present algorithmic improvements to the overlap Hybrid Monte Carlo algorithm, including preconditioning techniques and improvements to the correction step, used when one of the eigenvalues of the Kernel operator changes sign, which is now O(\Delta t^2) exact.Comment: 6 pages, 3 figures; poster contribution at Lattice 2005(Algorithms and machines

Monopoles in Compact U(1) -- Anatomy of the Phase Transition

We present evidence that the existence of a first order phase transition in compact U(1) with Wilson action is not related to monopole loops wrapping around the toroidal lattice, as has been previously suggested. Our analysis is based on the suppression of such loops by `soft boundary conditions' that correspond to an infinitely large chemical potential for the monopoles on the boundary, during the updating process. It is observed that the double peak structure characteristic for the first order phase transition reappears at sufficiently large lattice sizes and separations from the lattice boundary.Comment: 8 pages, (color) ps-figures available via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/monopoles/figures.u

Monopole clusters and critical dynamics in four-dimensional U(1)

We investigate monopoles in four-dimensional compact U(1) with Wilson action. We focus our attention on monopole clusters as they can be identified unambiguously contrary to monopole loops. We locate the clusters and determine their properties near the U(1) phase transition. The Coulomb phase is characterized by several small clusters, whereas in the confined phase the small clusters coalesce to one large cluster filling up the whole system. We find that clusters winding around the periodic lattice are absent within both phases and during the transition. However, within the confined phase, we observe periodically closed monopole loops if cooling is applied.Comment: 3 pages, Wuppertal preprint WUB 93-3

QCD on \alpha-Clusters

It is shown that the 21264 Alpha processor can reach about 20% sustained efficiency for the inversion of the Wilson-Dirac operator. Since fast ethernet is not sufficient to get balancing between computation and communication on reasonable lattice- and system-sizes, an interconnection using Myrinet is discussed. We find a price/performance ratio comparable with state-of-the-art SIMD-systems for lattice QCD.Comment: LATTICE99(machines), 3 page

Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized Biconjugate Gradient Algorithm

The stabilized biconjugate gradient algorithm BiCGStab recently presented by van der Vorst is applied to the inversion of the lattice fermion operator in the Wilson formulation of lattice Quantum Chromodynamics. Its computational efficiency is tested in a comparative study against the conjugate gradient and minimal residual methods. Both for quenched gauge configurations at beta= 6.0 and gauge configurations with dynamical fermions at beta=5.4, we find BiCGStab to be superior to the other methods. BiCGStab turns out to be particularly useful in the chiral regime of small quark masses.Comment: 25 pages, WUB 94-1

Finite size scaling analysis of compact QED

We describe results of a high-statistics finite size scaling analysis of 4d compact U(1) lattice gauge theory with Wilson action at the phase transition point. Using a multicanonical hybrid Monte Carlo algorithm we generate data samples with more than 150 tunneling events between the metastable states of the system, on lattice sizes up to 18^4. We performed a first analysis within the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence for a first-order phase transition with a plaquette energy gap, G=0.02667(20), at a transition coupling, beta_T=1.011128(11).Comment: Lattice 2000 (Topics in Gauge Theories),6 pages, 6 figures, LaTe

Compact QED under scrutiny: it's first order

We report new results from our finite size scaling analysis of 4d compact pure U(1) gauge theory with Wilson action. Investigating several cumulants of the plaquette energy within the Borgs-Kotecky finite size scaling scheme we find strong evidence for a first-order phase transition and present a high precision value for the critical coupling in the thermodynamic limit.Comment: Lattice2002(Spin

FFT for the APE Parallel Computer

We present a parallel FFT algorithm for SIMD systems following the `Transpose Algorithm' approach. The method is based on the assignment of the data field onto a 1-dimensional ring of systolic cells. The systolic array can be universally mapped onto any parallel system. In particular for systems with next-neighbour connectivity our method has the potential to improve the efficiency of matrix transposition by use of hyper-systolic communication. We have realized a scalable parallel FFT on the APE100/Quadrics massively parallel computer, where our implementation is part of a 2-dimensional hydrodynamics code for turbulence studies. A possible generalization to 4-dimensional FFT is presented, having in mind QCD applications.Comment: 17 pages, 13 figures, figures include

String breaking with dynamical Wilson fermions

We present results of our ongoing determination of string breaking in full QCD with N_f=2 Wilson fermions. Our investigation of the fission of the static quark-antiquark string into a static-light meson-antimeson system is based on dynamical configurations of size 24^3 x 40 produced by the TxL collaboration. Combining various optimization methods we determine the matrix elements of the two-by-two system with so far unprecedented accuracy. The all-to-all light quark propagators occurring in the transition element are computed from eigenmodes of the Hermitian Wilson-Dirac matrix complemented by stochastic estimates in the orthogonal subspace. We observe a clear signature for level-splitting between ground state and excited potential. Thus, for the first time, string breaking induced by sea quarks is observed in a simulation of 4-dimensional lattice-QCD.Comment: 3 pages, 3 figures, contribution to Lattice 200