Interface roughening in systems with quenched disorder

摘要

We present a theoretical framework for the discussion of the scaling properties of interfaces advancing in systems with quenched disorder. In all such systems there are critical conditions at which the interface gains scale invariance for sufficiently slow growth. There are two fundamental concepts, the ``blocking surfaces'' and the ``associated processes,'' whose nature determines the scaling properties of the advancing interfaces at criticality. The associated processes define a network whose scaling properties determine all the exponents (static and dynamic) that characterize the critical growing interface via universal scaling relations. We point out in this paper that most of the physical rules that can be used to advance the interface also incorporate noncritical elements; as a result, the roughness exponent of the growing interface may deviate from that of the critical interface in a rule-dependent way. We illustrate the wide applicability of the universal scaling relations with diverse models, such as the Edwards-Wilkinson (EW) model with quenched noise, the random-field Ising model, and the Kardar-Parisi-Zhang (KPZ) model with quenched noise. It is shown that the last model is characterized by bounded slopes, whereas in the EW model the slopes are unbounded. This fact makes the KPZ model equivalent to the self-organized interface depinning model of Buldyrev and Sneppen.