Anomalous Relaxation in the XY Gauge Glass

TL;DR

This study investigates the relaxation dynamics of the two-dimensional XY gauge glass, revealing a transition from exponential to algebraic decay at low temperatures and providing evidence for a finite-temperature glass transition.

Contribution

It presents direct integration of equations of motion for the XY gauge glass, characterizing relaxation times and identifying a potential finite-temperature glass transition.

Findings

Relaxation time diverges as T approaches T_g, indicating a glass transition.

Energy decay shifts from exponential at high T to algebraic at low T.

Vorticity decay explained by vortex annihilation dynamics.

Abstract

To study relaxation dynamics of the two-dimensional XY gauge glass, we integrate directly the equations of motion and investigate the energy function. As usual, it decays exponentially at high temperatures; at low but non-zero temperatures, it is found to exhibit an algebraic relaxation. We compute the relaxation time $\tau$ as a function of the temperature $T$ and find that the rapid increase of $\tau$ at low temperatures is well described by $\tau \sim (T-T_g)^{-b}$ with $T_g = 0.22 \pm 0.02$ and $b = 0.76 \pm 0.05$, which strongly suggests a finite-temperature glass transition. The decay of vorticity is also examined and explained in terms of a simple heuristic model, which attributes the fast relaxation at high temperatures to annihilation of unpinned vortices.