Writhe induced phase transition in unknotted self-avoiding polygons

TL;DR

This paper investigates how weighting the writhe in unknotted self-avoiding polygons can induce a phase transition, with implications for DNA experiments, supported by exact solutions and simulations showing a second-order transition under stretching.

Contribution

It provides the first exact solution for a directed model and demonstrates a phase transition in an undirected model through simulations, linking writhe weighting to physical phase behavior.

Findings

Exact solution for a directed model showing writhe-related phase transition.

Simulation results indicating a second-order phase transition in undirected polygons.

Transition becomes evident when polygons are sufficiently stretched with force.

Abstract

Recently it has been argued that weighting the writhe of unknotted self-avoiding polygons can be related to possible experiments that turn double stranded DNA. We first solve exactly a directed model and demonstrate that in such a subset of polygons the problem of weighting their writhe is associated with a phase transition. We then analyse simulations using the Wang-Landau algorithm to observe scaling in the fluctuations of the writhe that is compatible with a second-order phase transition in a undirected self-avoiding polygon model. Crucially, we conclude that the transition becomes apparent when the polygon is stretched sufficiently with a pulling force.