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We present a computer simulation study of the compact self-avoiding loops as regards their length and topological state. We use a Hamiltonian closed path on the cubic-shaped segment of a 3D cubic lattice as a model of a compact polymer. The importance of ergodic sampling of all loops is emphasized. We first look at the effect of global topological constraint on the local fractal geometry of a typical loop. We find that even short pieces of a compact trivial knot, or some other under-knotted loop, are somewhat crumpled compared to a topology-blind average over all loops. We further attempt to examine whether knots are localized or de-localized along the chain when the chain is compact. For this, we perform computational decimation and chain-coarsening, and look at the “renormalization trajectories” in the space of knots frequencies. Although not completely conclusive, our results are not inconsistent with the idea that knots become de-localized when the polymer is compact.

UNDER-KNOTTED AND OVER-KNOTTED POLYMERS 2: COMPACT SELF-AVOIDING LOOPS