Critical exponents for random knots

TL;DR

This paper demonstrates that the size scaling of zero-thickness polymer rings mirrors that of self-avoiding linear polymers, with implications for understanding knot sizes.

Contribution

It reveals that zero-thickness polymer rings scale similarly to self-avoiding polymers, providing new insights into knot size behavior.

Findings

Polymer ring size scales as N^ν with ν ≈ 0.588.

Size of trivial and non-trivial knots analyzed.

Scaling behavior parallels that of self-avoiding linear polymers.

Abstract

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.