Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory

We present results on the static $q\overline{q}$ potential from high-statistics simulations on ${16}^4$, ${24}^3$×32, and ${32}^4$ lattices, using the standard Wilson action at $\beta =6.0,6.2, \mathrm{and} 6.4$ on the Connection Machine CM2. To decrease noise and increase accuracy, we applied a suitable local smoothing technique on the spatial parts of Wilson loop operators. As a result, we find a violation of asymptotic scaling of the string tension, as signaled by $\frac{\sqrt{\sigma }}{{\Lambda }_L}=96.7\mathrm{}\left(1.6\right)\mathrm{}\left(2.6\right),86.4\mathrm{}\left(1.0\right)\mathrm{}\left(1.9\right),82.3\mathrm{}\left(0.8\right)\mathrm{}\left(1.7\right)\mathrm{}$, for the three $\beta$ values, with statistical and systematic errors. We observe a linear confining potential up to distances of 2 fm. A volume of ${\mathrm{}(1.5\mathrm{f}\mathrm{m})\mathrm{}}^3$ appears to be sufficient to avoid finite-size effects within our statistical accuracy (≅ 1%).