K. Akemi

Scaling study of pure gauge lattice QCD by Monte Carlo renormalization group method

The scaling behavior of pure gauge SU(3) in the region [beta]=5.85[minus]7.60 is examined by a Monte Carlo renormalization group analysis. The coupling shifts induced by factor 2 blocking are measured on both 32[sup 4] and 16[sup 4] lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all, of the deviation. It can be accounted for by a suitable change of coupling constant, including a correction term [ital O]([ital g][sup 7]) in the 2-loop lattice [beta] function. Based on this improvement, [radical][sigma] /[Lambda][sub M[bar S]][sup [ital n]][sub [ital f]]=0 is estimated to be 2.2[plus minus]0.1 from the analysis of the string tension [sigma].

QCD on the highly parallel computer AP1000

Abstract We have been running quenched QCD simulations on 32 4 and 32 3 × 48 lattices using a 512 processor AP1000, which is a highly parallel computer with up to 1024 processing elements. We have developed programs for update, blocking and hadron propagator calculations. The pseudo heatbath and the overrelaxation algorithms were used for the update with performance of 2.6 and 2.0 μsec/link, respectively.

Autocorrelation in updating pure SU(3) lattice gauge theory by the use of overrelaxed algorithms

Abstract We measure the sweep-to-sweep autocorrelations of blocked loops below and above the deconfinement transition for SU(3) on a 164 lattice using 20000–140000 Monte-Carlo updating sweeps. A divergence of the autocorrelation time toward the critical β is seen at high blocking levels. The peak is near β = 6.33 where we observe 440 ± 210 for the autocorrelation time of 1 × 1 Wilson loop on 24 blocked lattice. The mixing of 7 Brown-Woch overrelaxation steps followed by one pseudo-heat-bath step appears optimal to reduce the autocorrelation time below the critical β. Above the critical β, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.

QCD on the massively parallel computer AP1000

We present the QCD-TARO program of calculations which uses the parallel computer AP1000 of Fujitsu. We discuss the results on scaling, correlation times and hadronic spectrum, some aspects of the implementation and the future prospects.

Hadron spectroscopy on a 323 × 48 lattice

We report the first results of a hadron spectrum measurement by the QCD_TARO Collaboration with the massively parallel computer AP1000. The main memory of AP1000 is currently 8Gbytes (final goal : 16 Gbytes), which allows us to treat rather large lattices. We measure the quenched Wilson spectrum on a 323 × 48 lattice at β = 6.3. We obtain a good agreement with an empirical curve on the Edinburgh plot.

Systematic study of autocorrelation time in pure SU(3) lattice gauge theory

Abstract Results of our autocorrelation measurement performed on Fujitsu AP1000 are reported. We analyze (i) typical autocorrelation time, (ii) optimal mixing ratio between overrelaxation and pseudo-heatbath and (iii) critical behavior of autocorrelation time around cross-over region with high statistic in wide range of β for pure SU(3) lattice gauge theory on 8 4 , 16 4 and 32 4 lattices. For the mixing ratio K, small value (3–7) looks optimal in the confined region, and reduces the integrated autocorrelation time by a factor 2–4 compared to the pseudo-heatbath. On the other hand in the deconfined phase, correlation times are short, and overrelaxation does not seem to matter For a fixed value of K(=9 in this paper), the dynamical exponent of overrelaxation is close to 2. Autocorrelation measurement of the topological charge on 32 3 × 64 lattice at β = 6.0 is also briefly mentioned.

Monte Carlo renormalization group study at large β in confinement region

Abstract Monte Carlo renormalization group analysis on SU(3) lattice at large β is studied. On 32 4 lattice, coupling shift Δβ is 0.48 ± 0.02 and 0.53 ± 0.02 at β =6.55 and 6.80, where the lattice remains in confinement phase. Δβ is approaching its 2-loop asymptotic scaling value. However, deviation is still 20% and 13% at β =6.55 and 6.80, respectively. We also report high statistics data on 16 4 lattice at β =6.80, giving Δβ = .52 ± 0.03 in the deconfined regime.

Analyzing finite temperature mesonic correlators

We discuss problems related to the analysis of finite temperature general mesonic correlators and provide preliminary results on the pion wave function and dispersion law in quenched QCD at T ⋍ 0.9 Tc.

Does overrelaxed updating in lattice QCD improve critical slowing down

Abstract We study the autocorrelation time of blocked loops on 8 4 , 16 4 and 32 4 lattices in pure SU(3) lattice gauge theory over a wide range of β (= 6/ g 2 ) with high statistics. The critical exponent of integrated autocorrelation time by hybrid overrelaxation updating with fixed mixing ratio is found to be 1.74 ± 0.06. This suggests that the overrelaxation still suffer from critical slowing down toward the continuum limit.

Study of spatial size effect in quenched Wilson Hadron spectroscopy at β = 6.3

Abstract Quenched Wilson hadron spectroscopy at β = 6.3 has been studied by using parallel computer AP1000. Spectrum of hadrons composed of various combinations of hopping parameters are measured on 32 3 × 48 and 16 3 × 48 lattices. We report results of spatial size effects based on various hadron masses. Dependence on boundary conditions along the temporal direction is also examined and discussed.