Discretisation Errors in Landau Gauge on the Lattice

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which $\mathcal{O}(a^2)$ errors are removed is presented. $\mathcal{O}(a^2)$ improvement of the gauge fixing condition improves comparison with continuum Landau gauge in two ways: 1) through the elimination of $\mathcal{O}(a^2)$ errors and 2) through a secondary effect of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition.