Martin Hasenbusch

Speeding up the hybrid Monte Carlo algorithm for dynamical fermions

Abstract We propose a modification of the hybrid Monte Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is that the pseudo-fermion action is split into two parts. We test our proposal at the example of the two-dimensional lattice Schwinger model with two degenerate flavours of Wilson-fermions.

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.

Speeding up lattice QCD simulations with clover improved Wilson fermions

Abstract We apply a recent proposal to speed up the hybrid Monte Carlo simulation of systems with dynamical fermions to two flavour QCD with clover-improvement. The basic idea of our proposal is to split the fermion matrix into two factors with a reduced condition number each. In the effective action, for both factors a pseudo-fermion field is introduced. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.

Finite size scaling study of lattice models in the three-dimensional Ising universality class

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.

Theoretical estimates of the critical exponents of the superfluid transition in {sup 4}He by lattice methods

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class that apply to the superfluid transition in {sup 4}He along the {lambda} line of its phase diagram. We obtain the estimates {alpha}=-0.0151(3), {nu}=0.6717(1), {eta}=0.0381(2), {gamma}=1.3178(2), {beta}=0.3486(1), and {delta}=4.780(1). Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size L=128 and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent {alpha} disagrees with the most recent experimental estimate {alpha}=-0.0127(3) at the superfluid transition of {sup 4}He in a microgravity environment.

String effects in the Wilson loop: A High precision numerical test

Abstract We test numerically the effective string description of the infrared limit of lattice gauge theories in the confining regime. We consider the 3D Z 2 lattice gauge theory, and we define ratios of Wilson loops such that the predictions of the effective string theory do not contain any adjustable parameters. In this way we are able to obtain a degree of accuracy high enough to show unambiguously that the flux-tube fluctuations are described, in the infrared limit, by an effective bosonic string theory.

First results on the running coupling in QCD with two massless flavours

Abstract We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schrodinger functional scheme. The corresponding Λ-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic “experimentally” observable quantity. We find the non-perturbative evolution of the coupling important to eliminate a significant contribution to the total error in the estimated Λ-parameter.

String effects in the 3d gauge Ising model

We compare the predictions of the effective string description of confinement with a set of Montecarlo data for the 3d gauge Ising model at finite temperature. Thanks to a new algorithm which makes use of the dual symmetry of the model we can reach very high precisions even for large quark-antiquark distances. We are thus able to explore the large R regime of the effective string. We find that for large enough distances and low enough temperature the data are well described by a pure bosonic string. As the temperature increases higher order corrections become important and cannot be neglected even at large distances. These higher order corrections seem to be well described by the Nambu-Goto action truncated at the first perturbative order.

Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions

We compute an improved action for the Ising universality class in three dimensions that has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the