of the results in Sec. \[sec\_summ\].

Monopole cluster structure {#sec_cl_str}
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Background
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Fixing to the maximally Abelian gauge of SU(2) amounts to maximising with respect to gauge transformations the Morse functional R = - \_[n,]{} ( U\_(n) i\_3 U\^\_(n) i\_3 ). \[eqn\_R\] It is easy to see that this maximises the matrix elements $|[U_\mu(n)]_{11}|^2$ summed over all links. That is to say, it is the gauge in which the SU(2) link matrices are made to look as diagonal, and as Abelian, as possible — hence the name. Having fixed to this gauge, the link matrices are then written in a factored form and the U(1) link angle (just the phase of $[U_\mu(n)]_{11}$) is extracted. The U(1) field contains integer valued monopole currents [@degrand80], $\{ j_\mu(n) \}$, which satisfy a continuity relation, $\Delta_\mu j_\mu(n) = 0$, and may be unambiguously assigned to one of a set of mutually disconnected closed networks, or ‘clusters.’

In [@hart98] we found that the clusters may be divided into two classes on the basis of their length, where the length is obtained by simply summing the current in the cluster l = \_[n,]{} | j\_(n) |. The first class comprises the largest cluster, which is 