  We continue our numerical Monte Carlo simulation of a gas of closed loops on
a 3 dimensional lattice, however now in the presence of a topological term
added to the action corresponding to the total linking number between the
loops. We compute the linking number using certain notions from knot theory.
Adding the topological term converts the particles into anyons. Using the
correspondence that the model is an effective theory that describes the
2+1-dimensional Abelian Higgs model in the asymptotic strong coupling regime,
the topological linking number simply corresponds to the addition to the action
of the Chern-Simons term. We find the following new results. The system
continues to exhibit a phase transition as a function of the anyon mass as it
becomes small \cite{mnp}, although the phases do not change the manifestation
of the symmetry. The Chern-Simons term has no effect on the Wilson loop, but it
does affect the {\rm '}t Hooft loop. For a given configuration it adds the
linking number of the 't Hooft loop with all of the dynamical vortex loops to
the action. We find that both the Wilson loop and the 't Hooft loop exhibit a
perimeter law even though there are no massless particles in the theory, which
is unexpected.
