  In gauge systems coupled to matter, the static potential flattens out at a
scale where the confining string breaks by formation of a dynamical pair of
particles. Surprisingly, such a breaking is invisible in Wilson loops even when
the inter-charge separation is much larger than the flattening scale. Observing
string breaking also requires using different operators. A known string
mechanism provides us with a simple explanation, leading to the area law for
large Wilson loops, as observed in most gauge models coupled to whatever kind
of matter. It is also pointed out that in a simple 3D Z_2 gauge-Higgs model,
once reformulated in terms of Fortuin Kasteleyn clusters, this peculiar
behaviour of the Wilson operator can be ascribed to non-trivial linking of a
percolating cluster to the Wilson loop. Some numerical tests on this model are
also presented.
