AN IMPROVED GEOMETRIC ALGORITHM FOR CALCULATING THE TOPOLOGY OF LATTICE GAUGE-FIELDS

We implement the algorithm of Phillips and Stone on a hypercubic, periodic lattice and show that at currently accessible couplings the SU(2) topological charge so calculated is dominated by short-distance fluctuations. We propose and test an improvement to rid the measure of such lattice artifacts. We find that the improved algorithm produces a topological susceptibility that is consistent with that obtained by the alternative cooling method, thus resolving the controversial discrepancy between geometric and cooling methods. We briefly discuss the reasons for this and point out that our improvement is likely to be particularly effective when applied to the case of SU(3). © 1989