Collective roughening of elastic lines with hard core interaction in a disordered environment

TL;DR

This paper studies how elastic lines with hard-core interactions roughen in disordered environments, revealing logarithmic roughening in 2D and random walk behavior in 3D, with entanglement increasing with system height.

Contribution

It provides exact optimization analysis of elastic lines with disorder and hard-core interactions, highlighting dimensional differences in roughening behavior.

Findings

Logarithmic roughening in 2D systems.

Random walk-like behavior in 3D systems.

Entanglement increases with system height.

Abstract

We investigate by exact optimization methods the roughening of two and three-dimensional systems of elastic lines with point disorder and hard-core repulsion with open boundary conditions. In 2d we find logarithmic behavior whereas in 3d simple random walk-like behavior. The line 'forests' become asymptotically completely entangled as the system height is increased at fixed line density due to increasing line wandering.