Fluctuating loops and glassy dynamics of a pinned line in two dimensions

TL;DR

This paper models the glassy dynamics of a line in a 2D random landscape using independent two-state loops, providing an analytic description that aligns well with simulations and recent barrier scaling results.

Contribution

It introduces a novel representation of glassy line dynamics through independent loops, enabling analytical insights into complex slow dynamics.

Findings

Good agreement between analytic model and Monte Carlo simulations.

Barrier distributions scale as L^(1/3), consistent with recent findings.

The model captures fluctuations across all length scales.

Abstract

We represent the slow, glassy equilibrium dynamics of a line in a two-dimensional random potential landscape as driven by an array of asymptotically independent two-state systems, or loops, fluctuating on all length scales. The assumption of independence enables a fairly complete analytic description. We obtain good agreement with Monte Carlo simulations when the free energy barriers separating the two sides of a loop of size L are drawn from a distribution whose width and mean scale as L^(1/3), in agreement with recent results for scaling of such barriers.