Autocorrelation in Updating Pure SU(3) Lattice Gauge Theory by the use of Overrelaxed Algorithms

We measure the sweep-to-sweep autocorrelations of blocked loops below and above the deconfinement transition for SU(3) on a $16^4$ lattice using 20000-140000 Monte-Carlo updating sweeps. A divergence of the autocorrelation time toward the critical $\beta$ is seen at high blocking levels. The peak is near $\beta$ = 6.33 where we observe 440 $\pm$ 210 for the autocorrelation time of $1\times 1$ Wilson loop on $2^4$ 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 $\beta$. Above the critical $\beta$, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.Comment: 4 pages of A4 format including 6-figure

Temperature dependence of instantons in QCD

We investigate the temperature dependence of the instanton contents of gluon fields, using unquenched lattice QCD and the cooling method. The instanton size parameter deduced from the correlation function decreases from 0.44fm below the phase-transition temperature $T_c$ ($\approx 150$MeV) to 0.33fm at 1.3 $T_c$. The instanton charge distribution is Poissonian above $T_c$, but it deviates from the convoluted Poisson at low temperature. The topological susceptibility decreases rapidly below $T_c$, showing the apparent restoration of the $U(1)_A$ symmetry already at $T \approx T_c$.Comment: 8 pages TEX, 3 Postscript figures available at http://www.krl.caltech.edu/preprints/MAP.htm