  We examine the onset of classical topological order in a nearest-neighbor
kagome ice model. Using Monte Carlo simulations, we characterize the
topological sectors of the groundstate using a non-local cut measure which
circumscribes the toroidal geometry of the simulation cell. We demonstrate that
simulations which employ global loop updates that are allowed to wind around
the periodic boundaries cause the topological sector to fluctuate, while
restricted local loop updates freeze the simulation into one topological
sector. The freezing into one topological sector can also be observed in the
susceptibility of the real magnetic spin vectors projected onto the kagome
plane. The ability of the susceptibility to distinguish between fluctuating and
non-fluctuating topological sectors should motivate its use as a local probe of
topological order in a variety of related model and experimental systems.
