arXiv subjects
Publications and source records attributed to Ferenc Niedermayer.
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.
Due to its complex structure the parametrized fixed point action can not be simulated with the available local updating algorithms. We constructed, coded, and tested an updating procedure with 2+1 light flavors, where the targeted s-quark mass is at its physical value while the u- and d-quarks should produce pions lighter than 300MeV. In the algorithm a partially global gauge update is followed by several accept/reject steps, where parts of the determinant are switched on gradually in the order of their expenses. The trial configuration that is offered in the last, most expensive, stochastic accept/reject step differs from the original configuration by a Metropolis + over-relaxation gauge update over a sub-volume of ~(1.3 fm)^4. The acceptance rate in this accept/reject step is ~0.4. The code is optimized on different architectures and is running on lattices with L=1.2fm and 1.8fm at a resolution of a=0.15fm.
Our study on the cut-off effects in quenched light hadron spectroscopy and pion scattering length with the fixed point action is extended by results obtained at a lattice spacing a=0.102 fm in a box of size L=1.8 fm. The cut-off effects are small, but clearly seen as the resolution is increased from a=0.153 fm to a=0.102 fm. In the quark mass region where the errors are small and under control, our results on the APE plot lie close to the extrapolated numbers of the CP-PACS Collaboration.
Measurements of various physical quantities in the symmetry broken phase of the one component lattice $ϕ^4_4$ with standard action, are shown to be consistent with the critical behavior obtained by renormalization group analyses. This is in contrast to recent conclusions by another group, who further claim that the unconventional scaling behavior they observe, when extended to the complete Higgs sector of the Standard Model, would alter the conventional triviality bound on the mass of the Higgs.
We present results from quenched spectroscopy calculations with the parametrized fixed-point and the chirally improved Dirac operators. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. This allows us to work at small quark masses and we explore pseudoscalar-mass to vector-mass ratios down to 0.28. We discuss meson and baryon masses, their scaling properties, finite volume effects and compare our results with recent large scale simulations. We find that the size of quenching artifacts of the masses is strongly correlated with their experimentally observed widths and that the gauge and hadronic scales are consistent.
In this contribution we present results from quenched QCD simulations with the parameterized fixed-point (FP) and the chirally improved (CI) Dirac operator. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. We focus our discussion on observables sensitive to chirality. In particular we explore pion masses down to 210 MeV in light hadron spectroscopy, quenched chiral logs, the pion decay constant and the pion scattering length. We discuss finite volume effects, scaling properties of the FP and CI operators and performance issues in their numerical implementation.
We study the critical behaviour of the 2d dodecahedron spin model and investigate the conjecture that the discrete model describes the same continuum theory as the O(3) non-linear sigma model. In particular, we found that the anisotropy of the magnetization A(z) measured in a fixed physical volume decreases with increasing correlation length, at least up to ξ\approx 1000.
High precision measurements of the renormalized zero-momentum 4-point coupling g_R and of the Luscher-Weisz-Wolff running coupling gbar(L) = L*m(L) performed with two different lattice actions in the non-perturbative region confirm the earlier observations, that the cutoff effects look linear, in contrast to perturbative considerations. The use of different actions allows one to make a more reliable estimate on the continuum limit. The measurements were done for infinite volume correlation length up to 350.
We present a new parametrization of a SU(3) fixed point (FP) gauge action using smeared ("fat") gauge links. We report on the scaling behaviour of the FP action on coarse lattices by means of the static quark-antiquark potential, the hadronic scale $r_0$, the string tension $σ$ and the critical temperature $T_c$ of the deconfining phase transition. In addition, we investigate the low lying glueball masses where we observe no scaling violations within the statistical errors.
We study the behavior of asymptotically free (AF) spin and gauge models when their continuous symmetry group is replaced by different discrete non-Abelian subgroups. Precise numerical results with relative errors down to O(0.1%) suggest that the models with large subgroups are in the universality class of the underlying original models. We argue that such a scenario is consistent with the known properties of AF theories. The small statistical errors allow a detailed investigation of the cut-off effects also. At least up to correlation lengths ~300 they follow effectively an O(a) rather than the expected O(a^2) form both in the O(3) and in the dodecahedron model.
A new parametrization is introduced for the fixed point (FP) action in SU(3) gauge theory using fat links. We investigate its scaling properties by means of the static quark-antiquark potential and the dimensionless quantities $r_0 T_c, T_c/\sqrtσ$ and $r_0 \sqrtσ$, where $T_c$ is the critical temperature of the deconfining phase transition, $r_0$ is the hadronic scale and $σ$ is the effective string tension. These quantities scale even on lattices as coarse as $a \approx 0.3$ fm. We also measure the glueball spectrum and obtain $m_{0^{++}}=1627(83)$ MeV and $m_{2^{++}}=2354(95)$ MeV for the masses of the scalar and tensor glueballs, respectively.
The renormalized coupling $\gr$ defined through the connected 4-point function at zero external momentum in the non-linear O(3) sigma-model in two dimensions, is computed in the continuum form factor bootstrap approach with estimated error $\sim 0.3%$. New high precision data are presented for $\gr$ in the lattice regularized theory with standard action for nearly thermodynamic lattices $L/ξ\sim 7$ and correlation lengths $ξ$ up to $\sim 122$ and with the fixed point action for correlation lengths up to $\sim 12$. The agreement between the form factor and lattice results is within $\sim 1%$. We also recompute the phase shifts at low energy by measuring the two-particle energies at finite volume, a task which was previously performed by Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S-matrix is found.
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their properties. The possibility to define lattice chiral gauge theories is briefly discussed as well.
The fixed point Dirac operator on the lattice has exact chiral zero modes on topologically non-trivial gauge field configurations independently whether these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$, where $n_L$ $(n_R)$ is the number of left (right)-handed zero modes and $Q^{FP}$ is the fixed point topological charge holds not only in the continuum limit, but also at finite cut-off values. The fixed point action, which is determined by classical equations, is local, has no doublers and complies with the no-go theorems by being chirally non-symmetric. The index theorem is reproduced exactly, nevertheless. In addition, the fixed point Dirac operator has no small real eigenvalues except those at zero, i.e. there are no 'exceptional configurations'.
We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear $σ$ models with superinstanton boundary conditions is divergent in the limit of an infinite number of points $|Λ|$. This is the analogue of David's statement that renormalized perturbation theory of these models is infrared divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit $|Λ|\to\infty$ term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic, and free.
It has been pointed out in recent papers that the example considered earlier in the O(N) sigma-model to test whether fixed-point actions are 1-loop perfect actually checked classical perfection only. To clarify the issue we constructed the renormalized trajectory explicitly in 1-loop perturbation theory. We found that the fixed-point action is not exactly 1-loop perfect. The cut-off effects are, however, strongly reduced also on the 1-loop level relative to those of the standard and tree level improved Symanzik actions. Some points on off- and on-shell improvement, Symanzik's program and fixed-point actions are also discussed.
Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster and single--cluster methods, and of the standard and improved estimators are compared. (Lecture given at the summer school on `Advances in Computer Simulations', Budapest, July 1996.)
We present a new fixed point action for SU(3) lattice gauge theory, which has --- compared to earlier published fixed point actions --- shorter interaction range and smaller violations of rotational symmetry in the static $q\bar{q}$-potential even at shortest distances.