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=C1I exp{-C2[ln(I0/I)]1/2. The growth velocity VG of the surface of a disordered crystal is given by VG=c3Δμ exp{-C4[ln(Δμc/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