Interface Roughening in Systems with Quenched Random Impurities

The Schwartz-Villain model of anticorrelated quenched random fields interacting with the interface is considered in 2 dimensions via Burger's equation. For random field (anti-)-correlations decaying with a power law exponent 1 + 2μ, the model interpolates continuously between uncorrelated random fields, μ = 0, and random bonds impurities μ ⩾ 1. For μ < μc the roughening exponent ζ is ζ = 3/(3 + 2μ) in agreement with an Imry-Ma argument. For μ > μc, ζ turns out to be superuniversal ζ = 2/3 with μc = 3/4 from a one-loop calculation. The roughness amplitudes are calculated and their relation to domain wall interactions, pinning forces and interface velocity in driving field is stated.