  The bond-percolation properties of the Hanoi networks are analyzed with the
renormalization group. Unlike scale-free networks, they are meant to provide an
analytically tractable interpolation between finite dimensional, lattice-based
models and their mean-field limits. In percolation, the hierarchical
small-world bonds in the Hanoi networks impose a new form of order by uniting
otherwise disconnected, local clusters. This "patchy" order results in merely a
finite probability to obtain a spanning cluster for certain ranges of the bond
probability, unlike the usual 0-1 transition found on ordinary lattices. The
various networks studied here exhibit a range of phase behaviors, depending on
the prevalence of those long-range bonds. Fixed points in general exhibit
non-universal behavior.
