We study the systematic errors of Lüscher's formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite β. We confirm the existence of an optimal window in the cutoff parameter ε, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.

In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.

We present a study of the deconfinement phase transition of one-flavor QCD using the multiboson algorithm. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson method is a superior simulation algorithm. Finite-size scaling is studied on lattices of size 8 3 ϫ4, 12 3 ϫ4, and 16 3 ϫ4. The behaviors of the peak of the Polyakov loop susceptibility, the deconfinement ratio, and the distribution of the norm of the Polyakov loop are all characteristic of a first-order phase transition for heavy quarks. As the quark mass decreases, the first-order transition gets weaker and turns into a crossover. To investigate finite-size scaling on larger spatial lattices we use an effective action in the same universality class as QCD. This effective action is constructed by replacing the fermionic determinant with the Polyakov loop identified as the most relevant Z(3)-symmetry-breaking term. Higher-order effects are incorporated in an effective Z(3)-breaking field h, which couples to the Polyakov loop. Finite-size scaling determines the value of h where the first-order transition ends. Our analysis at the end point h ep indicates that the effective model and thus QCD are consistent with the universality class of the three-dimensional Ising model. Matching the field strength at the end point h ep to the values used in the dynamical quark simulations we estimate the end point ep of the first-order phase transition. We find ep ϳ0.08 which corresponds to a quark mass of about 1.4 GeV.

In a recent paper, Creutz has given a new action describing two species of Dirac fermions with exact chiral symmetry on the lattice. This action depends on parameters which may be fixed at certain values in order to get the right continuum limit.In this letter, we elaborate more on this idea and present an action which is free of any other parameter except the fermion mass.

We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.Comment: Revised version: 16 pages, 5 figures, algorithm adde