  We present a new type of cluster algorithm that strongly reduces critical
slowing down in simulations of vertex models. Since the clusters are closed
paths of bonds, we call it the {\em loop algorithm}. The basic steps in
constructing a cluster are the break-up and the freezing of vertices. We
concentrate on the case of the F model, which is a subset of the 6-vertex model
exhibiting a Kosterlitz-Thouless transition. The loop algorithm is also
applicable to simulations of other vertex models and of one and two-dimensional
quantum spin systems.
