Publication : t98/087

Abstract:
We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of polymer passing on top of each other. Each polygon configuration can be viewed as the two-dimensional projection of a particular knot. We study numerically the statistics of large polygons with a fixed knot type, using of a generalization of the BFACF algorithm for self-avoiding walks to account for the presence of crossings and to allow Reidemeister transformations preserving the knot topology. In the limit of a low crossing fugacity, we find a localization along the polygon of all the primary factors forming a knot. Increasing the crossing fugacity gives rise to a transition from a self-avoiding walk to a branched polymer behavior.

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