Thomas Jörg

Quenched spectroscopy with fixed-point and chirally improved fermions

Abstract 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.

THE CONSTRUCTION OF GENERALIZED DIRAC OPERATORS ON THE LATTICE

We discuss the steps to construct Dirac operators, which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.

Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and universality

We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p*, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.

Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents

Abstract In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D FP , see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate and the topological susceptibility χ t , and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions.

Cluster Monte Carlo Algorithms for Diluted Spin Glasses

Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin glass transition temperature. The application of such algorithms to the site-diluted EA model in three dimensions is discussed and the efficiency of the two algorithms is compared among each other and to parallel tempering. Finally, we give evidence for a spin glass transition in the three-dimensional site-diluted EA model with Gaussian couplings at a site occupation of p = 62.5%.Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin glass transition temperature. The application of such algorithms to the site-diluted EA model in three dimensions is discussed and the efficiency of the two algorithms is compared among each other and to parallel tempering. Finally, we give evidence for a spin glass transition in the three-dimensional site-diluted EA model with Gaussian couplings at a site occupation of p = 62.5%.

First results from a parametrized Fixed-Point QCD action

Abstract We have constructed a new fermion action which is an approximation to the (chirally symmetric) Fixed-Point action, containing the full Clifford algebra with couplings inside a hypercube and paths built from renormalization group inspired fat links. We present an exploratory study of the light hadron spectrum and the energy-momentum dispersion relation.

Progress using generalized lattice Dirac operators to parametrize the fixed point QCD action

Abstract We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all required symmetries. Optimizing a specific construction with hypercubic fermion offsets, we present some preliminary results.

Ultrametric probe of the spin-glass state in a field

We study the ultrametric structure of phase space of one-dimensional Ising spin glasses with random power-law interaction in an external random field. Although in zero field the model in both the mean-field and non-mean-field universality classes shows an ultrametric signature [Phys. Rev. Lett. 102, 037207 (2009)], when a field is applied ultrametricity seems only present in the mean-field regime. The results for the non-mean field case in an external field agree with data for spin glasses studied within the Migdal-Kadanoff approximation. Our results therefore suggest that the spin-glass state might be fragile to external fields below the upper critical dimension.

Quantum Chromodynamics with Chiral Quarks

Quantum-Chromodynamics (QCD) is the theory of quarks, gluons and their interaction. It has an important almost exact symmetry, the so-called chiral symmetry (which is actually broken spontaneously). This symmetry plays a major role in all low-energy hadronic processes. For traditional formulations of lattice QCD, CPU-time and memory limitations prevent simulations with light quarks and this symmetry is seriously violated. During the last years successful implementations of the chiral symmetry for lattice QCD have been constructed. We use two approximate implementations (both of them in the quenched approximation) with different specific advantages. We have also made progress towards the development of a practical algorithm to allow for simulations with dynamical quarks. In 2003 a series of discoveries of a new class of particles, called pentaquarks, has created very strong interest in lattice studies of resonance states. We have performed such studies with a specific method for the N* resonances with very satisfying results and are currently working on similar calculations for the pentaquarks. We have also addressed the question, which type of gauge field configurations is responsible for confinement and chiral symmetry breaking. Finally we are calculating three-point functions. We hope that for the small quark masses which we reach the results will not only be of direct phenomenological interest, but will also test predictions from chiral perturbation theory.