affected by the secondary clusters, and to do so using approximations that underestimate the effect of these smaller clusters. Consider an $R\times R$ Wilson loop. A monopole cluster that has an extent $r$ that is smaller then $R$ will affect it only weakly through higher multipole fields which cannot on their own give rise to an area law decay and a string tension. So we neglect such clusters and consider only those larger than $R$. Let us first neglect the observed breaking of scale invariance and simply assume that $r \propto \sqrt{l}$ and that $\gamma = 3$. We then find, by integrating eqn. \[eqn\_len\_spec\] and using eqn. \[eqn\_coeff\_spec\], that the number of secondary clusters with $r>R$ is proportional to $L^4 \sqrt{K}^{\zeta}/R^4$. We further assume that such clusters must be within a distance $\xi$ from the minimal surface of the Wilson loop, where $\xi$ is the screening length, if they are to disorder that loop significantly. The lattice volume this encompasses is the area of the planar loop, $R^2$, multiplied by a factor of $\xi$ for each of the two orthogonal directions in $d=4$. So the probability for this Wilson loop to be disordered thus decreases with $R$ as $(R^2\xi^2/L^4 \times 