arXiv subjects
Publications and source records attributed to Ulli Wolff.
We have calculated the step scaling function and the running coupling of QCD in the Schroedinger functional scheme with four flavors of O(a) improved Wilson quarks. Comparisons of our non-perturbative results with 2-loop and 3-loop perturbation theory as well as with non-perturbative data for only two flavors are made.
We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update scheme is proposed. Sample simulations are reported and the method turns out to be similarly efficient as the reflection cluster method, but it has greater potential for systematic generalization to other lattice field theories. A variant action suggested by the method is also simulated and leads to a rather extreme demonstration of the concept of universality of the scaling or continuum limit.
We exactly reformulate the lattice CP(N-1) spin model on a D dimensional torus as a loop model whose configurations correspond to the complete set of strong coupling graphs of the original system. A Monte Carlo algorithm is described and tested that samples the loop model with its configurations stored and manipulated as a linked list. Complete absence of critical slowing down and correspondingly small errors are found at D=2 for several observables including the mass gap. Using two different standard lattice actions universality is demonstrated in a finite size scaling study. The topological charge is identified in the loop model but not yet investigated numerically.
We have determined the non-perturbative O(a)-improvement coefficient c_sw for four flavors of Wilson quarks with the plaquette gauge action in a range of beta >= 5. The data are fitted with several Pade approximation formulae to get an impression of the stability. A small extrapolation below beta=5 seems acceptable.
We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross-Neveu model with Wilson fermions is simulated using the recent `worm' technique on the loop gas or all-order hopping representation of the fermions. An algorithm is formulated that includes the Gross-Neveu interaction for N fermion species. The critical line m_c(g) is constructed for a range of couplings at N = 6 and for N = 2, the Thirring model, as examples.
We report precise simulations of phi^4 theory in the Ising limit. A recent technique to stochastically evaluate the all-order strong coupling expansion is combined with exact identities in the closely related Aizenman random current representation. In this way high precision estimates of the renormalized coupling are possible at low CPU cost. As a sample application we present results for the unbroken phase of the Ising model in dimensions 3, 4 and 5 and investigate the question of triviality by studying a finite size scaling continuum limit.
We investigate the extension of the Prokof'ev-Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i. e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space-time dimensions. In D=2 Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D=3 the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.
We investigate in some detail an alternative simulation strategy for lattice field theory based on the so-called worm algorithm introduced by Prokof'ev and Svistunov in 2001. It amounts to stochastically simulating the strong coupling expansion rather than the usual configuration sum. A detailed error analysis and an important generalization of the method are exemplified here in the simple Ising model. It allows for estimates of the two point function where in spite of exponential decay the signal to noise ratio does not degrade at large separation. Critical slowing down is practically absent. In the outlook some thoughts on the general applicability of the method are offered.
We report on a scaling test of several mesonic observables in the non-perturbatively O(a) improved Wilson theory with two flavors of dynamical quarks. The observables are constructed in a fixed volume of 2.4fm x (1.8fm)^3 with Schroedinger functional boundary conditions. No significant scaling violations are found. Using the kaon mass determined in \cite{cernI}, we update our estimate of the Lambda parameter to Lambda^(2)_{msbar}/m_K = 0.52(6).
The (discrete) Gross-Neveu model is studied in a lattice realization with an N-component Majorana Wilson fermion field. It has an internal O(N) symmetry in addition to the euclidean lattice symmetries. The discrete chiral symmetry for vanishing mass is expected to emerge in the continuum limit only. The lattice theory is first recast in terms of two-valued bosonic link variables (dimers). In this representation, which coincides with the loop representation obtained earlier by Gattringer with the help of eight-vertex-models, the Boltzmann weight is essentially positive. While standard local updates are possible in this form we construct a further exact transformation where we generate dimer configurations as Peierls contours of an Ising model with a local action residing on plaquettes. For this model a Swendsen-Wang type cluster algorithm is constructed. At vanishing coupling it is numerically demonstrated to almost completely eliminate critical slowing down. Although further tests are required, an avenue to numerical studies of the Gross-Neveu model with unprecedented precision seems open.
We report on some preparatory investigations for the simulation of the QCD Schroedinger functional with a non-hermitian polynomial hybrid Monte Carlo algorithm. The complex spectrum of the non-hermitean free operator with SF boundary condititons is computed semianalytically. Then it is shown how one can obtain relevant information on the boundary of the spectral domain also in the presence of nontrivial gaugefields by monitoring the behavior of polynomials in the Wilson operator applied on random vectors.
We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As first applications, we derive ratios of the lambda parameters between the lattice scheme (improved gauge actions including six link loops) and the $\bar{\rm MS}$ scheme, and one-loop results for the Schroedinger functional coupling with a lattice $T=L \pm a$, which is motivated by considering staggered fermions.
For Majorana-Wilson lattice fermions in two dimensions we derive a dimer representation. This is equivalent to Gattringer's loop representation, but is made exact here on the torus. A subsequent dual mapping leads to yet another representation in which a highly efficient Swendsen-Wang type cluster algorithm is constructed. It includes the possibility of fluctuating boundary conditions. It also allows for improved estimators and makes interesting new observables accessible to Monte Carlo. The algorithm is compatible with the Gross-Neveu as well as an additional Z(2) gauge interaction. In this article numerical demonstrations are reported for critical free fermions.
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is argued to produce more certain error estimates than binning techniques and hence to help toward a better exploitation of expensive simulations. An effective integrated autocorrelation time is computed which is suitable to benchmark efficiencies of simulation algorithms with regard to specific observables of interest. A Matlab code is offered for download that implements the method. It can also combine independent runs (replica) allowing to judge their consistency.
We introduce a finite volume renormalization scheme for the N-Majorana-component O(N) invariant Gross-Neveu model. Universal observables are defined that are accessible to precise numerical simulation in various discretizations and allow for an extrapolation to the continuum limit. Here first numerical results with Wilson fermions are reported. For N=2 they reproduce exact finite volume continuum results in the massless Thirring model. Our N=8 data are ready for comparison for instance with staggered results in the future.
We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be kept under control, we find a variation of the integrated autocorrelation times by a factor of about two in the quantities of interest. Trajectories longer than conventionally used are found to be superior both in the Nf=0 and Nf=2 examples considered here. We also provide evidence that they lead to faster thermalization of systems with light quarks.
We investigate the two flavor chiral Gross-Neveu model in the Schroedinger functional on the lattice. The procedure necessary to recover chiral symmetry in the continuum limit of this model with Wilson fermions is discussed. We introduce several useful observables and present a first demonstration of the feasibility of Monte-Carlo simulations in this model.
We present results for the non-perturbative determination of the improvement and renormalization factors of the isovector axial current for lattice QCD with two flavors of dynamical Wilson quarks. The improvement and normalization conditions are formulated in terms of matrix elements of the PCAC relation in the Schroedinger functional setup and results are given in the form of interpolating formulae for bare gauge couplings beta=6/g_0^2>5.2.