Glassy dynamics of two-dimensional vortex glasses, charge-density waves, and surfaces of disordered crystals

The low-temperature phase of a model of pinned, two-dimensional flux lines is analytically shown to be glassy. Typical energy barriers L diverge as (lnL${)}^{1/2}$ as the length scale L→∞. This implies a voltage-current relation of the form V=${\mathit{C}}_1$I exp{-${\mathit{C}}_2$[ln(${\mathit{I}}_0$/I)${]}^{1/2}$. The growth velocity ${\mathit{V}}_{\mathit{G}}$ of the surface of a disordered crystal is given by ${\mathit{V}}_{\mathit{G}}$=${\mathit{c}}_3$Δμ exp{-${\mathit{C}}_4$[ln(Δ${\mathrm{\mu }}_{\mathit{c}}$/Δμ)${]}^{1/2}$}, where Δμ is the crystal-liquid chemical-potential difference. Similar results hold for 2D charge-density waves, if dislocations in the charge-density wave are ignored.