  We consider a network model, embedded on the Manhattan lattice, of a quantum
localisation problem belonging to symmetry class C. This arises in the context
of quasiparticle dynamics in disordered spin-singlet superconductors which are
invariant under spin rotations but not under time reversal. A mapping exists
between problems belonging to this symmetry class and certain classical random
walks which are self-avoiding and have attractive interactions; we exploit this
equivalence, using a study of the classical random walks to gain information
about the corresponding quantum problem. In a field-theoretic approach, we show
that the interactions may flow to one of two possible strong coupling regimes
separated by a transition: however, using Monte Carlo simulations we show that
the walks are in fact always compact two-dimensional objects with a
well-defined one-dimensional surface, indicating that the corresponding quantum
system is localised.
