Entanglement transition of elastic lines in a strongly disordered environment

TL;DR

This paper studies how elastic lines in a disordered environment become entangled as the system height increases, revealing a percolation transition in their connectivity.

Contribution

It provides the first numerical evidence of a percolation transition in the entanglement of elastic lines with point disorder.

Findings

Entanglement clusters span the system at a critical height.

The transition belongs to the ordinary percolation universality class.

The study uses exact optimization to analyze geometrical properties.

Abstract

We investigate by exact optimization the geometrical properties of three-dimensional elastic line systems with point disorder and hard-core repulsion. The line 'forests' become entangled due to increasing line wandering as the system height is increased, at fixed line density. There is a transition height at which a cluster of pairwise entangled lines spans the system, transverse to average line orientation. Numerical evidence implies that the phenomenon is in the ordinary percolation universality class.