  We study with lattice Monte Carlo simulations the relation of global O(2)
symmetry breaking in three dimensions to the properties of a geometrically
defined vortex loop network. We find that different definitions of constructing
a network lead to different results even in the thermodynamic limit, and that
with typical definitions the percolation transition does not coincide with the
thermodynamic phase transition. These results show that geometrically defined
percolation observables need not display universal properties related to the
critical behaviour of the system, and do not in general survive in the field
theory limit.
