12480798
Critical behavior of the two-dimensional XY model.
We present detailed Monte Carlo results for the susceptibility {chi}, correlation length {xi}, and specific heat {ital C}{sub {ital v}} for the {ital XY} model. The simulations are done on 64{sup 2}, 128{sup 2}, 256{sup 2}, and 512{sup 2} lattices over the temperature range 0.98{le}{ital T}{le}1.43 corresponding to 2{lt}{xi}{lt}70. Fits to {chi} and {xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values {nu}=0.5 and {eta}=0.25. Our best estimate, {ital T}{sub {ital c}}=0.894(5), is obtained using KT fits with {nu} fixed at 0.5. The exponent {eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find {eta}{approx}0.235 at {ital T}=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down.
15540297
Chiral limit of QCD
This talk contains an analysis of quenched chiral perturbation theory and its consequences. The chiral behavior of a number of quantities such as the pion mass m{sub pi}{sup 2}, the Bernard-Golterman ratios R and {sub X}, the masses of nucleons, and the kaon B-parameter are examined to see if the singular terms induced by the additional Goldstone boson, {eta}{prime}, are visible in present data. The overall conclusion (different from that presented at the lattice meeting) of this analysis is that even though there are some caveats attached to the indications of the extra terms induced by {eta}{prime} loops, the standard expressions break down when extrapolating the quenched data with m{sub q} < m{sub s}/2 to physical light quarks. I then show that due to the single and double poles in the quenched {eta}{prime}, the axial charge of the proton cannot be calculated using the Adler-Bell-Jackiw anomaly condition. I conclude with a review of the status of the calculation of light quark masses from lattice QCD.
122633786
Monte Carlo Renormalization Group: A Review
The logic and the methods of Monte Carlo Renormalization Group (MCRG) are reviewed. A status report of results for 4-dimensional lattice gauge theories derived using MCRG is presented. Existing methods for calculating the improved action are reviewed and evaluated. The Gupta-Cordery improved MCRG method is described and compared with the standard one.
124910471
Monte Carlo Renormalization Group for SU(2) Lattice Gauge Theory
We present the results of a Monte Carlo renormalization group calculation using the ..sqrt..3 block transformation introduced by Cordery, Gupta, and Novotny. The ..beta.. function for the SU(2) lattice gauge theory is calculated both along the Wilson axis and along the line K/sub A/ = -0.24K/sub F/ in the fundamental-adjoint plane.
18442234
Comparison of Inversion Algorithms for Wilson Fermions on the CM5
This talk presents results of a comparitive study of iterative algorithms like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCG\gamma_5$, and \bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the Connection Machine CM-5 using $32^3 \times 64$ lattices. The fermion action used is of Wilson type, both with and without the clover term. The overall conclusion is that preconditioned over-relaxed $MR$ is the simplest, uses the least memory, and is comparable in performance to \bicgstab. We find these two algorithms to be equally robust, $i.e.$ insensitive to the starting solution and to round-off errors.
121903104
Simulating QCD with dynamical Wilson and staggered fermions
Abstract I present a summary of the work done during the last year by the Los Alamos lattice collaboration (C. Baillie, R. Gupta, G. Kilcup, G. Guralnik, A. Patel and S. Sharpe) to study QCD with the Hybrid Monte Carlo Algorithm. The specific questions we have addressed are the finite temperature transition for both staggered and Wilson fermions and screening in the heavy q q potential with Wilson fermions. I also present a discussion of the efficiency of the fermion update algorithm.
39485818
Nucleus-nucleus potential from fusion and elastic scattering.
An analytical expression for the calculation of the nucleus-nucleus potential has been derived from an empirical formula which describes the fusion excitation function. The nucleus-nucleus potentials calculated for the projectiles /sup 6/Li, /sup 9/Be, and /sup 12/C in the interaction region --3--6.5 fm by the above procedure agree remarkably well with the real part of the respective optical potentials determined from the analysis of elastic scattering data which exhibit the ''rainbow'' phenomenon.
1943581
Quark confinement in quantum chromodynamics.
A quark-confinement mechanism inspired by renormalization-group-improved perturbative quantum chromodynamics is proposed. We obtain a quark-antiquark confining potential in the lowest approximation, show that it yields reasonable results for the bb-bar and cc-bar spin-averaged energy levels, and comment on the significance of the higher-order effects.
43411058
Semirelativistic potential model for heavy quarkonia.
The c-italicc-bar, b-italicb-bar, and t-italic t-italic-bar spectra are investigated with the use of a semirelativistic potential model described in an earlier paper. Results for the energy levels, leptonic widths, and E-italic1 transition widths are compared with the experimental data for c-italicc-bar and b-italicb-bar and predicted for t-italic t-italic-bar. We also find that the quark-antiquark interaction can best be described by a quasistatic rather than a momentum-dependent potential, and propose a theoretical justification for this surprising conclusion.
27549292
Isoscalar axial-vector renormalization constant and polarized proton structure function.
The isoscalar axial-vector renormalization constant is reevaluated using the QCD sum-rule method. It is found to be substantially different from the anomaly-free octet axial-vector u¯γμγ5+d¯γμγ5-2s¯γμγ5 coupling. Combining this determination with the known values of the isovector coupling GA and the F/D ratio for the octet current, we find the integral of the polarized proton structure function to be Gp=Fgp1(x)dx=0.135, in agreement with recent measurement by the European Muon Collaboration.
6552264
Nonsingular potential model for heavy quarkonia.
A nonsingular potential model for heavy quarkonia is described which does not require recourse to an illegitimate perturbative treatment for the investigation of quarkonium spectra. Our overall results for the energy levels, the leptonic widths, and the E1 transition widths are in very good agreement with the experimental data for bb-bar and they are reasonably good for cc-bar. We also find that the confining part of the quarkonium potential is scalar-vector exchange rather than the currently favored scalar exchange.