Interface depinning and directed polymer in quenched noises

Interface pinning–depinning transition in quenched random media is studied by investigating a simple directed polymer model with external driving force F. The directed polymer model can be described by a quenched Kardar–Parisi–Zhang (KPZ) equation. In our model, the velocity on a tilted initial condition follows v(m,f) fθ(1−m2) for small m, where m and f are the over all slope of the interface and the reduced force, respectively. The coefficient λ of the KPZ nonlinear term is proportional to −v and it approaches zero as F→Fc. We find that the roughness exponent α=1.00±0.02 in d=1+1 and α=0.92±0.05 in d=2+1 at the transition point. The transverse fluctuation of the polymer is also measured to determine the dynamic exponent z.