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A. Duncan

Publications and source records attributed to A. Duncan.

At least 37 records · Page 2Linked to original sources
arXiv2000

Anomalous Chiral Behavior in Quenched Lattice QCD

A study of the chiral behavior of pseudoscalar masses and decay constants is carried out in quenched lattice QCD with Wilson fermions. Using the modified quenched approximation (MQA) to cure the exceptional configuration problem, accurate results are obtained for pion masses as low as $\approx$ 200 MeV. The anomalous chiral log effect associated with quenched $η'$ loops is studied in both the relation between $m_π^2$ vs. $m_q$ and in the light-mass behavior of the pseudoscalar and axial vector matrix elements. The size of these effects agrees quantitatively with a direct measurement of the $η'$ hairpin graph, as well as with a measurement of the topological susceptibility, thus providing several independent and quantitatively consistent determinations of the quenched chiral log parameter $δ$. For $β=5.7$ with clover-improved fermions $(C_{sw} =1.57)$ all results are consistent with $δ=0.065\pm 0.013$ .

hep-lat↗
arXiv2000

On the reliability of mean-field methods in polymer statistical mechanics

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mean-field theory (LMFT) method to statistically exact results from two independent numerical Monte Carlo simulations for the problems of a polymer chain moving in a spherical cavity and a polymer chain partitioning between two confining spheres of different radii. It is shown that in some cases the agreement between the LMFT and the simulation results is excellent, while in others, such as the case of strongly fluctuating monomer repulsion fields, the LMFT results agree with the simulations only qualitatively. Various approximations of the LMFT method are systematically estimated, and the quantitative discrepancy between the two sets of results is explained with the diminished accuracy of the saddle-point approximation, implicit in the mean-field method, in the case of strongly fluctuating fields.

cond-mat.soft↗
arXiv1999

Partitioning of a polymer chain between two confining cavities: the role of electrostatic interactions

A recently developed lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E {\bf{60}}, 4257, (1999)] is generalized to the case where ground-state dominance in the polymer's Green's function does not apply. The full mean-field equations for the system are derived and are shown to possess a unique solution. The approach is applied to the problem of a charged Gaussian polymer chain confined to move within the region defined by two fused spheres. The failure of the notion of ground-state dominance under certain conditions even in the limit of large number of monomers is demonstrated.

cond-mat.stat-mech↗
arXiv1999

Chiral Effects of Quenched Eta-Prime Loops

Preliminary results of a study of quenched chiral logarithms at beta=5.7 are presented. Four independent determinations of the quenched chiral log parameter delta are obtained. Two of these are from estimates of the eta-prime mass, one from the residue of the hairpin diagram and the other from the topological susceptibility combined with the Witten-Veneziano formula. The other two determinations of delta are from measurement of virtual eta-prime loop effects in mpi^2 vs. quark mass and in the chiral behavior of the pseudoscalar decay constant. All results are consistent with delta=.080(15). The expected absence of quenched chiral logs in the axial-vector decay constant is also observed.

hep-lat↗
arXiv1999

Physical Effects of Infrared Quark Eigenmodes in LQCD

A truncated determinant algorithm is used to study the physical effects of the quark eigenmodes associated with eigenvalues below 400 MeV. This initial study focuses on coarse lattices (with O(a^2) improved gauge action), light internal quark masses and large physical volumes. Four bellwether full QCD processes are discussed: topological charge distributions, the eta prime propagator, string breaking as observed in the static energy and the rho decay into two pions.

hep-lat↗
arXiv1999

Modelling the Quark Determinant in Full QCD Simulations

The computational requirements and dynamics of Monte Carlo simulations of unquenched QCD incorporating the infrared quark eigenmodes (up to $\approx Λ_{QCD}$) exactly and UV modes via a loop representation are discussed. The accuracy of such a loop representation is studied for a variety of lattice volumes and quark masses. The method has been successfully applied for lattices up to 10$^3$x20 at $a \simeq$0.17F with improved (clover) action, and allows simulations at or near kappa critical.

hep-lat↗
arXiv1999

Statistical Mechanics of Charged Polymers in Electrolyte Solutions: A Lattice Field Theory Approach

The lattice field theory approach to the statistical mechanics of a classical Coulomb gas [R. Coalson and A. Duncan, J. Chem. Phys. 97,5653(1992)] is generalized to include charged polymer chains. Saddle-point analysis is done on the functional integral representing the partition function of the full system. Mean-field level analysis requires extremization of a real-valued functional with a single minimum, thus guaranteeing a unique solution. The full mean-field equations for such a coupled system are derived, as well as the leading (one-loop) fluctuation corrections. Two different numerical real-space lattice procedures are developed to implement the generalized theory; these are applied to the problem of a charged polymer confined to a spherical cavity in an electrolyte solution. The results provide new insight into the physics of confined polyelectrolytes.

cond-mat↗
arXiv1999

Loop Representations of the Quark Determinant in Lattice QCD

The modelling of the ultraviolet contributions to the quark determinant in lattice QCD in terms of a small number of Wilson loops is examined. Complete Dirac spectra are obtained for sizeable ensembles of SU(3) gauge fields at $β$=5.7 on 6$^4$, 8$^4$, and 10$^4$ lattices allowing for the first time a detailed study of the volume dependence of the effective loop action generating the quark determinant. The connection to the hopping parameter expansion is examined in the heavy quark limit. We compare the efficiency and accuracy of various methods- specifically, Lanczos versus stochastic approaches- for extracting the quark determinant on an ensemble of configurations.

hep-lat↗
arXiv1998

Evidence for quenched chiral logs

Using the pole shifting procedure of the modified quenched approximation (MQA) to cure the exceptional configuration problem, accurate hadron hadron spectrum calculations can be obtained at very light quark mass. Here we use the MQA to extend and improve our previous investigation of chiral logs in the pion mass. At beta=5.7 for Wilson fermion, we see clear evidence for quenched chiral logarithms in the pion mass as a function of quark mass. The size of the observed chiral log exponent delta is in good agreement with the value obtained from a direct calculation of the eta' hairpin diagram.

hep-lat↗
arXiv1998

Truncated Determinant Approach to Light Dynamical Quarks

Virtual quark effects in lattice QCD are studied in an approach where the infrared modes are included in a precise and gauge-invariant manner. At fixed physical volume the required number of modes does not increase in the continuum limit, and the acceptance is tolerable even for very light quark masses. Topological charge distributions at varying quark mass, and the static quark potential, showing the onset of string-breaking, are presented in both QED2 and QCD4.

hep-lat↗
arXiv1998

An Efficient Algorithm for QCD with Light Dynamical Quarks

A new approach to the inclusion of virtual quark effects in lattice QCD simulations is presented. Infrared modes which build in the chiral physics in the light quark mass limit are included exactly and in a gauge invariant way. At fixed physical volume the number of relevant infrared modes does not increase as the continuum limit is approached. The acceptance of our procedure does not decrease substantially in the limit of small quark masses. Two alternative approaches are discussed for including systematically the remaining ultraviolet modes. In particular, we present evidence that these modes are accurately described by an effective action involving only small Wilson loops.

hep-lat↗
arXiv1998

Quenched Chiral Artifacts for Wilson-Dirac Fermions

We examine artifacts associated with the chiral symmetry breaking induced through the use of Wilson-Dirac fermions in lattice Monte Carlo computations. For light quark masses, the conventional quenched theory can not be defined using direct Monte Carlo methods due to the existence of nonintegrable poles in physical quantities. These poles are associated with the real eigenvalue spectrum of the Wilson-Dirac operator. We show how this singularity structure can be observed in the analysis of both QED in two dimensions and QCD in four dimensions.

hep-lat↗
arXiv1997

The eta-prime propagator in quenched QCD

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa<kappa_c in the quark propagators to the critical value of hop ping parameter. By this method, the eta-prime propagator can be accurately calculated even for very light quark mass. A determination of the topological susceptibility for quenched QCD is also obtained, using the fermionic method of Smit and Vink to calculate winding numbers.

hep-lat↗
arXiv1997

Resolving Exceptional Configurations

In lattice QCD with Wilson fermions, exceptional configurations arise in the quenched approximation at small quark mass. The origin of these large previously uncontrolled lattice artifacts is identified. A simple well-defined procedure (MQA) is presented which removes the artifacts while preserving the correct continuum limit.

hep-lat↗
arXiv1997

QED2 as a testbed for interpolations between quenched and full QCD

Lattice QED2 with the Wilson formulation of fermions is used as a convenient model system to study artifacts of the quenched approximation on a finite lattice. The quenched functional integral is shown to be ill-defined in this system as a consequence of the appearance of exactly real modes for physical values of the fermion mass. The location and frequency of such modes is studied as a function of lattice spacing, lattice volume, topological charge and improved action parameters. The efficacy of the recently proposed modified quenched approximation is examined, as well as a new approach to the interpolation from the quenched to full dynamical theory employing a truncated form of the fermion determinant.

hep-lat↗
arXiv1997

Quenched Approximation Artifacts: A study in 2-dimensional QED

The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional integral is shown to be extremely compicated, with multiple branch points and cuts. The connection of lattice topological charge and exactly real eigenmodes is explored using cooling techniques. The lattice volume and spacing dependence of these modes is studied, as is the effect of clover improvement of the action. A recently proposed modified quenched approximation is applied to the study of meson correlators, and the results compared with both naive quenched and full dynamical calculations of the same quantity.

hep-lat↗
arXiv1997

Gauge Invariant Effective Potentials and Higgs Mass Bounds

The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite gauge invariant order parameter in physical gauges. This effective potential is computed through one loop order in a model with scalars and fermions coupled to an abelian gauge theory, which serves as a simple model of the situation in electroweak theory, where vacuum stability arguments based on the scalar effective potential have been used to place lower bounds on the Higgs mass.

hep-ph↗