Fractional Inversion in Krylov Space

The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for $M^\gamma x = b$ in Krylov space. In case of $\gamma = 1/2$, the expansion is in terms of Legendre polynomials, and rigorous bounds for the truncation error are derived.Comment: Contribution to LAT97 proceedings, 3 page

Study of a new simulation algorithm for dynamical quarks on the APE-100 parallel computer

First results on the autocorrelation behaviour of a recently proposed fermion algorithm by M. L\"uscher are presented and discussed. The occurence of unexpected large autocorrelation times is explained. Possible improvements are discussed.Comment: 3 pages, compressed ps-file (uufiles), Contribution to Lattice 9

Two-flavour Schwinger model with dynamical fermions in the L\"uscher formalism

We report preliminary results for 2D massive QED with two flavours of Wilson fermions, using the Hermitean variant of L\"uscher's bosonization technique. The chiral condensate and meson masses are obtained. The simplicity of the model allows for high statistics simulations close to the chiral and continuum limit, both in the quenched approximation and with dynamical fermions.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 3 Postscript figures, uses twoside, fleqn, espcrc2, epsf, revised version (details of approx. polynomial

Computing the lowest eigenvalues of the Fermion matrix by subspace iterations

Subspace iterations are used to minimise a generalised Ritz functional of a large, sparse Hermitean matrix. In this way, the lowest $m$ eigenvalues are determined. Tests with $1 \leq m \leq 32$ demonstrate that the computational cost (no. of matrix multiplies) does not increase substantially with $m$. This implies that, as compared to the case of a $m=1$, the additional eigenvalues are obtained for free.Comment: Talk presented at LATTICE96(algorithms), 3 pages, 2 Postscript figures, uses epsf.sty, espcrc2.st

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

Locality with staggered fermions

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes. A definition of such a theory necessitates an underlying local fermion operator with the same determinant and the corresponding Green's functions to establish causality and unitarity. We illustrate this point by studying analytically and numerically the square root of the staggered fermion operator. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.Comment: 24 pages, 7 figures, few remarks added for clarity, accepted for publication in Nucl. Phys.

The locality problem for two tastes of staggered fermions

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes from four to two. We study analytically and numerically the square root of the staggered fermion operator as a candidate to define a two taste theory from first principles. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.Comment: Talk presented at Lattice2004(theory), Fermilab, June 21-26, 200

Improvements of the local bosonic algorithm

We report on several improvements of the local bosonic algorithm proposed by M. Luescher. We find that preconditioning and over-relaxation works very well. A detailed comparison between the bosonic and the Kramers-algorithms shows comparable performance for the physical situation examined.Comment: Talk presented at LATTICE96(algorithms), 3 pages, Latex, espcrc

Four-dimensional Simulation of the Hot Electroweak Phase Transition with the SU(2) Gauge-Higgs Model

We study the finite-temperature phase transition of the four-dimensional SU(2) gauge-Higgs model for intermediate values of the Higgs boson mass in the range 50 \lsim m_H \lsim 100GeV on a lattice with the temporal lattice size $N_t=2$. The order of the transition is systematically examined using finite size scaling methods. Behavior of the interface tension and the latent heat for an increasing Higgs boson mass is also investigated.Comment: Talk presented at LATTICE96(electroweak), 3 pages of LaTeX, 4 PostScript figure

Universality in the Gross-Neveu model

We consider universal finite size effects in the large-N limit of the continuum Gross-Neveu model as well as in its discretized versions with Wilson and with staggered fermions. After extrapolation to zero lattice spacing the lattice results are compared to the continuum values.Comment: Lattice2004(theory