Abelian projections using other gauges. In our case we can overcome this problem by going to a large enough volume that the physically relevant percolating cluster can be simply identified. \[The reason this cannot be done with other typical Abelian gauge fixings is that there the unphysical monopoles are dense on lattice scales making any meaningful separation into clusters impossible.\] We can then extract the string tension using, in our Wilson loop calculation, only this largest monopole cluster. The fact that the length of this cluster scales in physical units, with apparently no significant anomalous dimension, tells us that this calculation will not be drowned in ultraviolet ‘noise’ as we approach the continuum limit. Of course, the fact that we can only do this for volumes that diverge in physical units as $a\to 0$ is a symptom of the underlying breakdown of the Abelian projection.

The qualitative discussion in the previous paragraph over-estimates the effect of the secondary clusters; for example, the contribution that a cluster of fixed size in lattice units makes to a Wilson loop of a fixed physical size will clearly go to zero as $a\to 0$. So it is useful to ask how Wilson loops are 